Liliana Guran | Babes-Bolyai University (original) (raw)

Papers by Liliana Guran

Research paper thumbnail of Comparative analysis of various approaches to evaluating the parameters of multidimensional models

The problem of evaluating parameters of a multidimensional model according to measurement results... more The problem of evaluating parameters of a multidimensional model according to measurement results is examined. The conditions on which the problem solution depends are itemized.

Research paper thumbnail of Fixed Point Theorems for Multivalued Contractive Operators on Generalized Metric Spaces

Using the concept of generalized w-distance we prove some interesting results on the existence of... more Using the concept of generalized w-distance we prove some interesting results on the existence of fixed points for multivalued contractive type operators in the setting of generalizes metric spaces. A data dependence result and Ulam-Hyers stability of fixed point inclusions are also presented.

Research paper thumbnail of Fixed point problems concerning contractive type operators on KST-Spaces

Carpathian Journal of Mathematics, 2018

In this paper, using the concept of w-distance we prove some results on the existence of fixed po... more In this paper, using the concept of w-distance we prove some results on the existence of fixed points for contractive type operators, namely; (α, µ)-ψ-contractive operators. Applications are also presented. Our results improve and generalize a number of known results of fixed point theory including the recent results of Guran and Bota [ Guran, L. and Bota, M.-F., Ulam-Hyers Stability Problems for Fixed Point Theorems concerning α-ψ-Type Contractive Operators on KST-Spaces, Submitted in press.] and Ansari [Ansari, A. H. and Shukla, S., Some fixed point theorems for ordered F-(F , h)-contraction and subcontractions in θ-f-orbitally complete partial metric spaces, J.

Research paper thumbnail of Complex-valued double controlled metric like spaces with applications to fixed point theorems and Fredholm type integral equations

AIMS Mathematics

In this paper we introduce the concept of complex-valued double controlled metric like spaces. Th... more In this paper we introduce the concept of complex-valued double controlled metric like spaces. These new results generalize and extend the corresponding results about complex-valued double controlled metric type spaces. We prove some complex-valued fixed point theorems in this new complex-valued metric like spaces and, as application, we give an existence and uniqueness of the solution of a Fredholm type integral equation result. Moreover, some examples are also presented in favor of our given results.

Research paper thumbnail of Fixed point theory in complex valued controlled metric spaces with an application

AIMS Mathematics

In this article we have introduced a metric named complex valued controlled metric type space, mo... more In this article we have introduced a metric named complex valued controlled metric type space, more generalized form of controlled metric type spaces. This concept is a new extension of the concept complex valued $ b −metrictypespaceandthisoneisdifferentfromcomplexvaluedextended-metric type space and this one is different from complex valued extended −metrictypespaceandthisoneisdifferentfromcomplexvaluedextended b $-metric space. Using the idea of this new metric, some fixed point theorems involving Banach, Kannan and Fisher contractions type are proved. Some examples togetheran application are described to sustain our primary results.

Research paper thumbnail of Fixed point problems concerning contractive type operators on KST-Spaces

Carpathian Journal of Mathematics, 2018

In this paper, using the concept of w-distance we prove some results on the existence of fixed po... more In this paper, using the concept of w-distance we prove some results on the existence of fixed points for contractive type operators, namely; (α, µ)-ψ-contractive operators. Applications are also presented. Our results improve and generalize a number of known results of fixed point theory including the recent results of Guran and Bota [ Guran, L. and Bota, M.-F., Ulam-Hyers Stability Problems for Fixed Point Theorems concerning α-ψ-Type Contractive Operators on KST-Spaces, Submitted in press.] and Ansari [Ansari, A. H. and Shukla, S., Some fixed point theorems for ordered F-(F, h)-contraction and subcontractions in θ-f-orbitally complete partial metric spaces, J. Adv. Math. Stud., 9 (2016), No. 1, 37–53].

Research paper thumbnail of Using computational techniques of fixed point theory for studying the stationary infinite horizon problem from the financial field

AIMS mathematics, Dec 31, 2022

Research paper thumbnail of A new approach of overlapping generation model via fixed point technique

AIMS mathematics, Dec 31, 2023

Research paper thumbnail of Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications

Fractal and fractional, Oct 18, 2023

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Research paper thumbnail of Computational comparative analysis of fixed point approximations of generalized $ \alpha $-nonexpansive mappings in hyperbolic spaces

AIMS mathematics, 2023

In this article, we use the Picard-Thakur hybrid iterative scheme to approximate the fixed points... more In this article, we use the Picard-Thakur hybrid iterative scheme to approximate the fixed points of generalized $ \alpha −nonexpansivemappings.Forgeneralized-nonexpansive mappings. For generalized −nonexpansivemappings.Forgeneralized \alpha −nonexpansivemappingsinhyperbolicspaces,weshowseveralweakandstrongconvergenceresults.ItisprovednumericallyandgraphicallythatthePicard−Thakurhybriditerativeschemeconvergesmorefasterthanotherwell−knownhybriditerativemethodsforgeneralized-nonexpansive mappings in hyperbolic spaces, we show several weak and strong convergence results. It is proved numerically and graphically that the Picard-Thakur hybrid iterative scheme converges more faster than other well-known hybrid iterative methods for generalized −nonexpansivemappingsinhyperbolicspaces,weshowseveralweakandstrongconvergenceresults.ItisprovednumericallyandgraphicallythatthePicard−Thakurhybriditerativeschemeconvergesmorefasterthanotherwell−knownhybriditerativemethodsforgeneralized \alpha $-nonexpansive mappings. We also present an application to Fredholm integral equation.

Research paper thumbnail of On the dynamics of a dual space–time fractional nonlinear Schrödinger model in optical fibers

Results in physics, Aug 1, 2023

Research paper thumbnail of A Novel Approach for the Approximate Solution of Wave Problems in Multi-Dimensional Orders with Computational Applications

Axioms, Nov 24, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Research paper thumbnail of Remarks on Fractal-Fractional Malkus Waterwheel Model with Computational Analysis

Symmetry, Oct 21, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Research paper thumbnail of Fixed points and coupled fixed points in <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>b</mi></mrow><annotation encoding="application/x-tex">b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">b</span></span></span></span>-metric spaces via graphical contractions

Carpathian Journal of Mathematics, Jul 30, 2022

In this paper some existence and stability results for cyclic graphical contractions in complete ... more In this paper some existence and stability results for cyclic graphical contractions in complete metric spaces are given. An application to a coupled fixed point problem is also derived. (2) closed if for each sequence (x n) n∈N in Y which converges to an element x, we have x ∈ Y. The b-metric space (M, d) is complete if every Cauchy sequence from M converges in X. Lemma 1.1. Notice that in a b-metric space (M, d) the following assertions hold: (i) a convergent sequence has a unique limit; (ii) each convergent sequence is Cauchy. Although, there are some important distance-type differences: the b-metric on M need not be continuous, open balls in b-metric spaces need not be open sets, the closed ball is not necessary a closed set, to recall few.

Research paper thumbnail of Computational Study for Fiber Bragg Gratings with Dispersive Reflectivity Using Fractional Derivative

Fractal and Fractional

In this paper, the new representations of optical wave solutions to fiber Bragg gratings with cub... more In this paper, the new representations of optical wave solutions to fiber Bragg gratings with cubic–quartic dispersive reflectivity having the Kerr law of nonlinear refractive index structure are retrieved with high accuracy. The residual power series technique is used to derive power series solutions to this model. The fractional derivative is taken in Caputo’s sense. The residual power series technique (RPST) provides the approximate solutions in truncated series form for specified initial conditions. By using three test applications, the efficiency and validity of the employed technique are demonstrated. By considering the suitable values of parameters, the power series solutions are illustrated by sketching 2D, 3D, and contour profiles. The analysis of the obtained results reveals that the RPST is a significant addition to exploring the dynamics of sustainable and smooth optical wave propagation across long distances through optical fibers.

Research paper thumbnail of On Intuitionistic Fuzzy Nb Metric Space and Related Fixed Point Results with Application to Nonlinear Fractional Differential Equations

Fractal and Fractional

This manuscript contains several new notions including intuitionistic fuzzy Nb metric space, intu... more This manuscript contains several new notions including intuitionistic fuzzy Nb metric space, intuitionistic fuzzy quasi-Sb-metric space, intuitionistic fuzzy pseudo-Sb-metric space, intuitionistic fuzzy quasi-N-metric space and intuitionistic fuzzy pseudo Nb fuzzy metric space. We prove decomposition theorem and fixed-point results in the setting of intuitionistic fuzzy pseudo Nb fuzzy metric space. Further, we provide several non-trivial examples to show the validity of introduced notions and results. At the end, we solve an integral equation, system of linear equations and nonlinear fractional differential equations as applications.

Research paper thumbnail of Stability, Data Dependence, and Convergence Results with Computational Engendering of Fractals via Jungck–DK Iterative Scheme

Fractal and Fractional

We have developed a Jungck version of the DK iterative scheme called the Jungck–DK iterative sche... more We have developed a Jungck version of the DK iterative scheme called the Jungck–DK iterative scheme. Our analysis focuses on the convergence and stability of the Jungck–DK scheme for a pair of non-self-mappings using the more general contractive condition. We demonstrate that this iterative scheme converges faster than all other leading Jungck-type iterative schemes. To further illustrate its effectiveness, we provide an example to verify the rate of convergence and prove the data dependence result for the Jungck–DK iterative scheme. Finally, we calculate the escape criteria for generating Mandelbrot and Julia sets for polynomial functions and present visually appealing images of these sets by our modified iteration.

Research paper thumbnail of A Study on Medical Diagnostic Approach to Investigate Cardiac Diseases

Lecture notes in networks and systems, 2022

Research paper thumbnail of Computational comparative analysis of fixed point approximations of generalized $ \alpha $-nonexpansive mappings in hyperbolic spaces

AIMS Mathematics

In this article, we use the Picard-Thakur hybrid iterative scheme to approximate the fixed points... more In this article, we use the Picard-Thakur hybrid iterative scheme to approximate the fixed points of generalized $ \alpha −nonexpansivemappings.Forgeneralized-nonexpansive mappings. For generalized −nonexpansivemappings.Forgeneralized \alpha −nonexpansivemappingsinhyperbolicspaces,weshowseveralweakandstrongconvergenceresults.ItisprovednumericallyandgraphicallythatthePicard−Thakurhybriditerativeschemeconvergesmorefasterthanotherwell−knownhybriditerativemethodsforgeneralized-nonexpansive mappings in hyperbolic spaces, we show several weak and strong convergence results. It is proved numerically and graphically that the Picard-Thakur hybrid iterative scheme converges more faster than other well-known hybrid iterative methods for generalized −nonexpansivemappingsinhyperbolicspaces,weshowseveralweakandstrongconvergenceresults.ItisprovednumericallyandgraphicallythatthePicard−Thakurhybriditerativeschemeconvergesmorefasterthanotherwell−knownhybriditerativemethodsforgeneralized \alpha $-nonexpansive mappings. We also present an application to Fredholm integral equation.

Research paper thumbnail of On Graphical Fuzzy Metric Spaces with Application to Fractional Differential Equations

Fractal and Fractional

In this article, the authors introduced the concept of graphical fuzzy metric spaces which is a g... more In this article, the authors introduced the concept of graphical fuzzy metric spaces which is a generalization of fuzzy metric spaces with the help of a relation. The authors discussed some topological structure, convergence criteria, and proved a Banach fixed-point result in graphical fuzzy metric space. As an application of obtained results, the authors find a solution of an integral equation and nonlinear fractional differential equations in the context of graphical fuzzy metric spaces. The authors provided some examples to illustrate the obtained results herein.

Research paper thumbnail of Comparative analysis of various approaches to evaluating the parameters of multidimensional models

The problem of evaluating parameters of a multidimensional model according to measurement results... more The problem of evaluating parameters of a multidimensional model according to measurement results is examined. The conditions on which the problem solution depends are itemized.

Research paper thumbnail of Fixed Point Theorems for Multivalued Contractive Operators on Generalized Metric Spaces

Using the concept of generalized w-distance we prove some interesting results on the existence of... more Using the concept of generalized w-distance we prove some interesting results on the existence of fixed points for multivalued contractive type operators in the setting of generalizes metric spaces. A data dependence result and Ulam-Hyers stability of fixed point inclusions are also presented.

Research paper thumbnail of Fixed point problems concerning contractive type operators on KST-Spaces

Carpathian Journal of Mathematics, 2018

In this paper, using the concept of w-distance we prove some results on the existence of fixed po... more In this paper, using the concept of w-distance we prove some results on the existence of fixed points for contractive type operators, namely; (α, µ)-ψ-contractive operators. Applications are also presented. Our results improve and generalize a number of known results of fixed point theory including the recent results of Guran and Bota [ Guran, L. and Bota, M.-F., Ulam-Hyers Stability Problems for Fixed Point Theorems concerning α-ψ-Type Contractive Operators on KST-Spaces, Submitted in press.] and Ansari [Ansari, A. H. and Shukla, S., Some fixed point theorems for ordered F-(F , h)-contraction and subcontractions in θ-f-orbitally complete partial metric spaces, J.

Research paper thumbnail of Complex-valued double controlled metric like spaces with applications to fixed point theorems and Fredholm type integral equations

AIMS Mathematics

In this paper we introduce the concept of complex-valued double controlled metric like spaces. Th... more In this paper we introduce the concept of complex-valued double controlled metric like spaces. These new results generalize and extend the corresponding results about complex-valued double controlled metric type spaces. We prove some complex-valued fixed point theorems in this new complex-valued metric like spaces and, as application, we give an existence and uniqueness of the solution of a Fredholm type integral equation result. Moreover, some examples are also presented in favor of our given results.

Research paper thumbnail of Fixed point theory in complex valued controlled metric spaces with an application

AIMS Mathematics

In this article we have introduced a metric named complex valued controlled metric type space, mo... more In this article we have introduced a metric named complex valued controlled metric type space, more generalized form of controlled metric type spaces. This concept is a new extension of the concept complex valued $ b −metrictypespaceandthisoneisdifferentfromcomplexvaluedextended-metric type space and this one is different from complex valued extended −metrictypespaceandthisoneisdifferentfromcomplexvaluedextended b $-metric space. Using the idea of this new metric, some fixed point theorems involving Banach, Kannan and Fisher contractions type are proved. Some examples togetheran application are described to sustain our primary results.

Research paper thumbnail of Fixed point problems concerning contractive type operators on KST-Spaces

Carpathian Journal of Mathematics, 2018

In this paper, using the concept of w-distance we prove some results on the existence of fixed po... more In this paper, using the concept of w-distance we prove some results on the existence of fixed points for contractive type operators, namely; (α, µ)-ψ-contractive operators. Applications are also presented. Our results improve and generalize a number of known results of fixed point theory including the recent results of Guran and Bota [ Guran, L. and Bota, M.-F., Ulam-Hyers Stability Problems for Fixed Point Theorems concerning α-ψ-Type Contractive Operators on KST-Spaces, Submitted in press.] and Ansari [Ansari, A. H. and Shukla, S., Some fixed point theorems for ordered F-(F, h)-contraction and subcontractions in θ-f-orbitally complete partial metric spaces, J. Adv. Math. Stud., 9 (2016), No. 1, 37–53].

Research paper thumbnail of Using computational techniques of fixed point theory for studying the stationary infinite horizon problem from the financial field

AIMS mathematics, Dec 31, 2022

Research paper thumbnail of A new approach of overlapping generation model via fixed point technique

AIMS mathematics, Dec 31, 2023

Research paper thumbnail of Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications

Fractal and fractional, Oct 18, 2023

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Research paper thumbnail of Computational comparative analysis of fixed point approximations of generalized $ \alpha $-nonexpansive mappings in hyperbolic spaces

AIMS mathematics, 2023

In this article, we use the Picard-Thakur hybrid iterative scheme to approximate the fixed points... more In this article, we use the Picard-Thakur hybrid iterative scheme to approximate the fixed points of generalized $ \alpha −nonexpansivemappings.Forgeneralized-nonexpansive mappings. For generalized −nonexpansivemappings.Forgeneralized \alpha −nonexpansivemappingsinhyperbolicspaces,weshowseveralweakandstrongconvergenceresults.ItisprovednumericallyandgraphicallythatthePicard−Thakurhybriditerativeschemeconvergesmorefasterthanotherwell−knownhybriditerativemethodsforgeneralized-nonexpansive mappings in hyperbolic spaces, we show several weak and strong convergence results. It is proved numerically and graphically that the Picard-Thakur hybrid iterative scheme converges more faster than other well-known hybrid iterative methods for generalized −nonexpansivemappingsinhyperbolicspaces,weshowseveralweakandstrongconvergenceresults.ItisprovednumericallyandgraphicallythatthePicard−Thakurhybriditerativeschemeconvergesmorefasterthanotherwell−knownhybriditerativemethodsforgeneralized \alpha $-nonexpansive mappings. We also present an application to Fredholm integral equation.

Research paper thumbnail of On the dynamics of a dual space–time fractional nonlinear Schrödinger model in optical fibers

Results in physics, Aug 1, 2023

Research paper thumbnail of A Novel Approach for the Approximate Solution of Wave Problems in Multi-Dimensional Orders with Computational Applications

Axioms, Nov 24, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Research paper thumbnail of Remarks on Fractal-Fractional Malkus Waterwheel Model with Computational Analysis

Symmetry, Oct 21, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Research paper thumbnail of Fixed points and coupled fixed points in <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>b</mi></mrow><annotation encoding="application/x-tex">b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">b</span></span></span></span>-metric spaces via graphical contractions

Carpathian Journal of Mathematics, Jul 30, 2022

In this paper some existence and stability results for cyclic graphical contractions in complete ... more In this paper some existence and stability results for cyclic graphical contractions in complete metric spaces are given. An application to a coupled fixed point problem is also derived. (2) closed if for each sequence (x n) n∈N in Y which converges to an element x, we have x ∈ Y. The b-metric space (M, d) is complete if every Cauchy sequence from M converges in X. Lemma 1.1. Notice that in a b-metric space (M, d) the following assertions hold: (i) a convergent sequence has a unique limit; (ii) each convergent sequence is Cauchy. Although, there are some important distance-type differences: the b-metric on M need not be continuous, open balls in b-metric spaces need not be open sets, the closed ball is not necessary a closed set, to recall few.

Research paper thumbnail of Computational Study for Fiber Bragg Gratings with Dispersive Reflectivity Using Fractional Derivative

Fractal and Fractional

In this paper, the new representations of optical wave solutions to fiber Bragg gratings with cub... more In this paper, the new representations of optical wave solutions to fiber Bragg gratings with cubic–quartic dispersive reflectivity having the Kerr law of nonlinear refractive index structure are retrieved with high accuracy. The residual power series technique is used to derive power series solutions to this model. The fractional derivative is taken in Caputo’s sense. The residual power series technique (RPST) provides the approximate solutions in truncated series form for specified initial conditions. By using three test applications, the efficiency and validity of the employed technique are demonstrated. By considering the suitable values of parameters, the power series solutions are illustrated by sketching 2D, 3D, and contour profiles. The analysis of the obtained results reveals that the RPST is a significant addition to exploring the dynamics of sustainable and smooth optical wave propagation across long distances through optical fibers.

Research paper thumbnail of On Intuitionistic Fuzzy Nb Metric Space and Related Fixed Point Results with Application to Nonlinear Fractional Differential Equations

Fractal and Fractional

This manuscript contains several new notions including intuitionistic fuzzy Nb metric space, intu... more This manuscript contains several new notions including intuitionistic fuzzy Nb metric space, intuitionistic fuzzy quasi-Sb-metric space, intuitionistic fuzzy pseudo-Sb-metric space, intuitionistic fuzzy quasi-N-metric space and intuitionistic fuzzy pseudo Nb fuzzy metric space. We prove decomposition theorem and fixed-point results in the setting of intuitionistic fuzzy pseudo Nb fuzzy metric space. Further, we provide several non-trivial examples to show the validity of introduced notions and results. At the end, we solve an integral equation, system of linear equations and nonlinear fractional differential equations as applications.

Research paper thumbnail of Stability, Data Dependence, and Convergence Results with Computational Engendering of Fractals via Jungck–DK Iterative Scheme

Fractal and Fractional

We have developed a Jungck version of the DK iterative scheme called the Jungck–DK iterative sche... more We have developed a Jungck version of the DK iterative scheme called the Jungck–DK iterative scheme. Our analysis focuses on the convergence and stability of the Jungck–DK scheme for a pair of non-self-mappings using the more general contractive condition. We demonstrate that this iterative scheme converges faster than all other leading Jungck-type iterative schemes. To further illustrate its effectiveness, we provide an example to verify the rate of convergence and prove the data dependence result for the Jungck–DK iterative scheme. Finally, we calculate the escape criteria for generating Mandelbrot and Julia sets for polynomial functions and present visually appealing images of these sets by our modified iteration.

Research paper thumbnail of A Study on Medical Diagnostic Approach to Investigate Cardiac Diseases

Lecture notes in networks and systems, 2022

Research paper thumbnail of Computational comparative analysis of fixed point approximations of generalized $ \alpha $-nonexpansive mappings in hyperbolic spaces

AIMS Mathematics

In this article, we use the Picard-Thakur hybrid iterative scheme to approximate the fixed points... more In this article, we use the Picard-Thakur hybrid iterative scheme to approximate the fixed points of generalized $ \alpha −nonexpansivemappings.Forgeneralized-nonexpansive mappings. For generalized −nonexpansivemappings.Forgeneralized \alpha −nonexpansivemappingsinhyperbolicspaces,weshowseveralweakandstrongconvergenceresults.ItisprovednumericallyandgraphicallythatthePicard−Thakurhybriditerativeschemeconvergesmorefasterthanotherwell−knownhybriditerativemethodsforgeneralized-nonexpansive mappings in hyperbolic spaces, we show several weak and strong convergence results. It is proved numerically and graphically that the Picard-Thakur hybrid iterative scheme converges more faster than other well-known hybrid iterative methods for generalized −nonexpansivemappingsinhyperbolicspaces,weshowseveralweakandstrongconvergenceresults.ItisprovednumericallyandgraphicallythatthePicard−Thakurhybriditerativeschemeconvergesmorefasterthanotherwell−knownhybriditerativemethodsforgeneralized \alpha $-nonexpansive mappings. We also present an application to Fredholm integral equation.

Research paper thumbnail of On Graphical Fuzzy Metric Spaces with Application to Fractional Differential Equations

Fractal and Fractional

In this article, the authors introduced the concept of graphical fuzzy metric spaces which is a g... more In this article, the authors introduced the concept of graphical fuzzy metric spaces which is a generalization of fuzzy metric spaces with the help of a relation. The authors discussed some topological structure, convergence criteria, and proved a Banach fixed-point result in graphical fuzzy metric space. As an application of obtained results, the authors find a solution of an integral equation and nonlinear fractional differential equations in the context of graphical fuzzy metric spaces. The authors provided some examples to illustrate the obtained results herein.