Jatinderdeep Kaur - Academia.edu (original) (raw)
Papers by Jatinderdeep Kaur
Journal of Advances in Mathematics and Computer Science
In the paper [Some new observations on Geraghty and \(\acute{C}\)iri\(\acute{c}\) type results in... more In the paper [Some new observations on Geraghty and \(\acute{C}\)iri\(\acute{c}\) type results in b-metric spaces, Mathematics, 7, (2019), doi: 10.3390/math7070643] Mlaiki et al. introduced (\(\alpha\), \(\beta\))-type contraction in order to generalize the contraction mapping defined by Pant and Panicker. Also, in the paper [Some fixed point results in b- metric spaces and b-metric-like spaces with new contractive mappings, Axioms, 10(2), (2021), 15 pages, doi: 10.3390/axioms10020055] Jain and Kaur presented the concepts of \(\xi\) -contractive mappings. Now, the aim of the present article is to introduce \(\xi\) - (\(\alpha\), \(\beta\)) -contractive mappings in b-metric spaces by combining the concepts (\(\alpha\), \(\beta\))-type contraction and \(\xi\)-contractive mappings. Also, we establish some fixed point results for newly defined mappings. Our results generalize various theorems in literature. In support, we provide an example.
... healthy discussions, suggestions and necessary co-operation to complete this work. Yes, I am ... more ... healthy discussions, suggestions and necessary co-operation to complete this work. Yes, I am also grateful to my parents and my husband S. Rupinder Pal Singh for their patience and love. ... doctoral work. September, 2009 (Jatinderdeep Kaur) Page 5. ABSTRACT ...
Proceedings of the Estonian Academy of Sciences, 2019
In the present paper, we extend the concept of contraction in a new manner by introducing D-contr... more In the present paper, we extend the concept of contraction in a new manner by introducing D-contraction defined on a family F of bounded functions. We also introduce a new notion of a fixed function on a metric space. Some fixed function theorems along with illustrative examples and application are also given to verify the effectiveness of our results.
The present dissertation entitled, “Fixed Points of Contraction Mappings on Metric and G-Metric S... more The present dissertation entitled, “Fixed Points of Contraction Mappings on Metric and G-Metric Spaces”, contains a brief account of investigations carried out by various authors and by me on existence of fixed points of self mappings in metric space under the supervision of Dr. Jatinderdeep Kaur, Assistant Professor, School of Mathematices and Computer Applications, Thapar University, Patiala. The aim of this work is to study and obtain some result on existence and uniqueness of fixed points. Fixed point theory has wide ranging application in many areas of mathematics. For example, in finding the solution of the system of linear equations, in proving the existence of solutions of ordinary and differential equation, integral equations, analysis and many other disciplines. The whole work is divided into three chapters. Chapter I is introduction which includes brief account of definitions and results which will be required for the later chapters. In Chapter II, we have studied Banach ...
The intent of this dissertation entitled “Existence of Fixed Points for Some Mappings in Various ... more The intent of this dissertation entitled “Existence of Fixed Points for Some Mappings in Various Generalized Metric Spaces” embodies a brief account of investigation carried out by authors on existence of fixed points of self mappings in various metric spaces under the supervision of Dr. Jatinderdeep Kaur, Assistant Professor, School of Mathematics, Thapar University, Patiala. The aim of this work is to study and obtain some result on existence and uniqueness of fixed points. Fixed point theory is one of the most powerful tool in nonlinear analysis. Fixed point theory has wide ranging application in many area of mathematics. For example, in finding the solution of the system of linear equations, in proving the existence of solutions of ordinary and partial differential equation, integral equations, analysis and many other disciplines. The whole work is divided into four chapters. Chapter I is introduction which includes brief account of definitions and results which will be required...
The intent of this dissertation entitled “Existence of Fixed Points for Some Mappings in Various ... more The intent of this dissertation entitled “Existence of Fixed Points for Some Mappings in Various Generalized Metric Spaces” embodies a brief account of investigation carried out by authors on existence of fixed points of self mappings in various metric spaces under the supervision of Dr. Jatinderdeep Kaur, Assistant Professor, School of Mathematics, Thapar University, Patiala. The aim of this work is to study and obtain some result on existence and uniqueness of fixed points. Fixed point theory is one of the most powerful tool in nonlinear analysis. Fixed point theory has wide ranging application in many area of mathematics. For example, in finding the solution of the system of linear equations, in proving the existence of solutions of ordinary and partial differential equation, integral equations, analysis and many other disciplines. The whole work is divided into four chapters. Chapter I is introduction which includes brief account of definitions and results which will be required for the later chapters. In Chapter II, we have studied Fixed point theorem for α−ψ contractive mapping which guarantees the existence and uniqueness of fixed point in b-metric spaces. The aim of Chapter III is to study common fixed point results for weakly isotone increasing mapping in partially ordered b-metric-like space. Chapter IV is concerned with common fixed theorems using newly defined contractive type mappings for partially ordered b-metric-like space. Moreover, corollary is obtained in this chapter. At the end, we have have presented some references of research papers and books cited in the dissertation.
World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, 2016
The existence of sine and cosine series as a Fourier series, their L-convergence seems to be one ... more The existence of sine and cosine series as a Fourier series, their L-convergence seems to be one of the difficult question in theory of convergence of trigonometric series in L-metric norm. In the literature so far available, various authors have studied the L-convergence of cosine and sine trigonometric series with special coefficients. In this paper, we present a modified cosine and sine sums and criterion for L-convergence of these modified sums is obtained. Also, a necessary and sufficient condition for the L-convergence of the cosine and sine series is deduced as corollaries. Keywords—Conjugate Dirichlet kernel, Dirichlet kernel, L-convergence, modified sums.
A very interesting approach in the theory of contractive mappings was recently given by Samet et ... more A very interesting approach in the theory of contractive mappings was recently given by Samet et al. (Nonlinear Anal. 75, 2012, 2154-2165) by using the concept of α-ψ contractive type mappings in metric spaces. The purpose of this paper is to give the generalized version of α-ψ contractive type mappings in complex valued metric spaces. For this, we define the notion of (α, φ)-contractive mappings of rational type and obtain fixed point theorems for such mappings in the framework of complex valued metric spaces. This extends and subsumes the recent results of Azam et al. (Numerical Functional Analysis and optimization 32, 2011, 243-253) and Rouzkard and Imdad (Computers and Mathematics with Applications 2012, doi:10.1016/j.camwa.2012.02.063) regarding common fixed point theorems in complex valued metric spaces. Also, we derive common coupled fixed point theorems in complete complex valued metric spaces. Our results generalize many previously obtained results. Some examples are presen...
In this paper, some estimates for Dirichlet kernel has been proved. Also, we have obtained the co... more In this paper, some estimates for Dirichlet kernel has been proved. Also, we have obtained the complex form of modified trigonometric cosine and sine sums of X.Z. Krasniqi (10) and have proved the convergence of complex trigonometric series under class J* of complex coefficients in metric space j j j n jx a a x x n i n n n n t n i n t n i n n n e c c n e c c n e c e c e c e c
In the present paper, the concept of contraction has been extended in a refined manner by introdu... more In the present paper, the concept of contraction has been extended in a refined manner by introducing mathfrakD\mathfrak{D}mathfrakD-Contraction defined on a family mathfrakF\mathfrak{F}mathfrakF of bounded functions. Also, a new notion of fixed function has been introduced for a metric space. Some fixed function theorems along with illustrative examples have also been given to verify the effectiveness of our results. In addition, an application to medical science has also been presented. This application is based on best approximation of treatment plan for tumor patients getting intensity modulated radiation therapy(IMRT). In this technique, a proper DDC matrix truncation has been used that significantly improves accuracy of results. In 2013, Z. Tian \textit{et al.} presented a fluence map optimization(FMO) model for dose calculation by splitting the DDC matrix into two components on the basis of a threshold intensity value. Following this concept, a sequence of functions can be constructed through the presented ...
The present dissertation entitled, “A Study of New Topologies on R” comprises certain investigati... more The present dissertation entitled, “A Study of New Topologies on R” comprises certain investigations carried out by me at School of Mathematics, Thapar University, Patiala, under the supervision of Dr. Jatinderdeep Kaur, Assistant Professor, School of Mathematics, Thapar University, Patiala. The aim of this work is to find new topologies with this new set of basis B− and B+. The topologies generated from this new set of basis are different from standard, lower limit, upper limit and k-topologies. We compared well known topologies with new topologies on R. The whole work is divided into four chapters. Chapter 1 is introduction which includes brief account of definitions and their examples which will be required for the later chapters. In chapter 2, we have studied some main theorems which guarantees how topology can be generated from given base and vice-versa. The aim of chapter 3 is to study well known topologies on R and their topological properties. In chapter 4, we introduced new...
The present dissertation entitled, “Integrability and L−convergence of Certain Trigonometric Seri... more The present dissertation entitled, “Integrability and L−convergence of Certain Trigonometric Series”, contains a brief account of investigations carried out by me on L−convergence of Trigonometric Cosine Series under the supervision of Dr. Jatinderdeep Kaur, Assistant Professor, School of Mathematics and Computer Applications, Thapar University, Patiala. The work presented in this dissertation has been divided into four chapters. The first chapter is introductory. In this chapter, apart from setting up the notations and terminology to be used in sequel, we have presented some known results. The purpose of chapter II is to study the integrability and L−convergence of Fourier cosine series. In chapter III, we studied the necessary and sufficient condition for the L−convergence of Rees-Stanojevic cosine sums. In chapter IV, we have studied the L−convergence of Ram-Kumari modified cosine sum. Towards the end, references of various publications cited in the present dissertation have been...
In this paper, the results of Kano from one dimensional cosine and sine series are extended to tw... more In this paper, the results of Kano from one dimensional cosine and sine series are extended to two dimensional cosine and sine series. To extend these results, some classes of coefficient sequences such as class of semi convexity and class R are extended from one dimension to two dimensions. Further, the function f(x, y) is two dimensional Fourier Cosine and Sine series or equivalently it represents an integrable function or not, has been studied. Moreover, some results are obtained which are generalization of Moricz’s results. Keywords—Conjugate Dirichlet kernel, conjugate Fejer kernel, Fourier series, Semi-convexity.
Applied General Topology, 2014
The notion of coupled fixed point was introduced by Guo and Laksmikantham [12]. Later Gnana Bhask... more The notion of coupled fixed point was introduced by Guo and Laksmikantham [12]. Later Gnana Bhaskar and Lakshmikantham in [11] investigated the coupled fixed points in the setting of partially ordered set by defining the notion of mixed monotone property. Very recently, the concept of tripled fixed point was introduced by Berinde and Borcut [7]. Following this trend, Karapınar[19] defined the quadruple fixed point. In this manuscript, quadruple fixed point is discussed and some new fixed point theorems are obtained on partial metric spaces.
In this paper, we extend the result of Ram (3) and also study the L 1 - convergence of the r th d... more In this paper, we extend the result of Ram (3) and also study the L 1 - convergence of the r th derivative of cosine series.
Journal of Advances in Mathematics and Computer Science
In the paper [Some new observations on Geraghty and \(\acute{C}\)iri\(\acute{c}\) type results in... more In the paper [Some new observations on Geraghty and \(\acute{C}\)iri\(\acute{c}\) type results in b-metric spaces, Mathematics, 7, (2019), doi: 10.3390/math7070643] Mlaiki et al. introduced (\(\alpha\), \(\beta\))-type contraction in order to generalize the contraction mapping defined by Pant and Panicker. Also, in the paper [Some fixed point results in b- metric spaces and b-metric-like spaces with new contractive mappings, Axioms, 10(2), (2021), 15 pages, doi: 10.3390/axioms10020055] Jain and Kaur presented the concepts of \(\xi\) -contractive mappings. Now, the aim of the present article is to introduce \(\xi\) - (\(\alpha\), \(\beta\)) -contractive mappings in b-metric spaces by combining the concepts (\(\alpha\), \(\beta\))-type contraction and \(\xi\)-contractive mappings. Also, we establish some fixed point results for newly defined mappings. Our results generalize various theorems in literature. In support, we provide an example.
... healthy discussions, suggestions and necessary co-operation to complete this work. Yes, I am ... more ... healthy discussions, suggestions and necessary co-operation to complete this work. Yes, I am also grateful to my parents and my husband S. Rupinder Pal Singh for their patience and love. ... doctoral work. September, 2009 (Jatinderdeep Kaur) Page 5. ABSTRACT ...
Proceedings of the Estonian Academy of Sciences, 2019
In the present paper, we extend the concept of contraction in a new manner by introducing D-contr... more In the present paper, we extend the concept of contraction in a new manner by introducing D-contraction defined on a family F of bounded functions. We also introduce a new notion of a fixed function on a metric space. Some fixed function theorems along with illustrative examples and application are also given to verify the effectiveness of our results.
The present dissertation entitled, “Fixed Points of Contraction Mappings on Metric and G-Metric S... more The present dissertation entitled, “Fixed Points of Contraction Mappings on Metric and G-Metric Spaces”, contains a brief account of investigations carried out by various authors and by me on existence of fixed points of self mappings in metric space under the supervision of Dr. Jatinderdeep Kaur, Assistant Professor, School of Mathematices and Computer Applications, Thapar University, Patiala. The aim of this work is to study and obtain some result on existence and uniqueness of fixed points. Fixed point theory has wide ranging application in many areas of mathematics. For example, in finding the solution of the system of linear equations, in proving the existence of solutions of ordinary and differential equation, integral equations, analysis and many other disciplines. The whole work is divided into three chapters. Chapter I is introduction which includes brief account of definitions and results which will be required for the later chapters. In Chapter II, we have studied Banach ...
The intent of this dissertation entitled “Existence of Fixed Points for Some Mappings in Various ... more The intent of this dissertation entitled “Existence of Fixed Points for Some Mappings in Various Generalized Metric Spaces” embodies a brief account of investigation carried out by authors on existence of fixed points of self mappings in various metric spaces under the supervision of Dr. Jatinderdeep Kaur, Assistant Professor, School of Mathematics, Thapar University, Patiala. The aim of this work is to study and obtain some result on existence and uniqueness of fixed points. Fixed point theory is one of the most powerful tool in nonlinear analysis. Fixed point theory has wide ranging application in many area of mathematics. For example, in finding the solution of the system of linear equations, in proving the existence of solutions of ordinary and partial differential equation, integral equations, analysis and many other disciplines. The whole work is divided into four chapters. Chapter I is introduction which includes brief account of definitions and results which will be required...
The intent of this dissertation entitled “Existence of Fixed Points for Some Mappings in Various ... more The intent of this dissertation entitled “Existence of Fixed Points for Some Mappings in Various Generalized Metric Spaces” embodies a brief account of investigation carried out by authors on existence of fixed points of self mappings in various metric spaces under the supervision of Dr. Jatinderdeep Kaur, Assistant Professor, School of Mathematics, Thapar University, Patiala. The aim of this work is to study and obtain some result on existence and uniqueness of fixed points. Fixed point theory is one of the most powerful tool in nonlinear analysis. Fixed point theory has wide ranging application in many area of mathematics. For example, in finding the solution of the system of linear equations, in proving the existence of solutions of ordinary and partial differential equation, integral equations, analysis and many other disciplines. The whole work is divided into four chapters. Chapter I is introduction which includes brief account of definitions and results which will be required for the later chapters. In Chapter II, we have studied Fixed point theorem for α−ψ contractive mapping which guarantees the existence and uniqueness of fixed point in b-metric spaces. The aim of Chapter III is to study common fixed point results for weakly isotone increasing mapping in partially ordered b-metric-like space. Chapter IV is concerned with common fixed theorems using newly defined contractive type mappings for partially ordered b-metric-like space. Moreover, corollary is obtained in this chapter. At the end, we have have presented some references of research papers and books cited in the dissertation.
World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, 2016
The existence of sine and cosine series as a Fourier series, their L-convergence seems to be one ... more The existence of sine and cosine series as a Fourier series, their L-convergence seems to be one of the difficult question in theory of convergence of trigonometric series in L-metric norm. In the literature so far available, various authors have studied the L-convergence of cosine and sine trigonometric series with special coefficients. In this paper, we present a modified cosine and sine sums and criterion for L-convergence of these modified sums is obtained. Also, a necessary and sufficient condition for the L-convergence of the cosine and sine series is deduced as corollaries. Keywords—Conjugate Dirichlet kernel, Dirichlet kernel, L-convergence, modified sums.
A very interesting approach in the theory of contractive mappings was recently given by Samet et ... more A very interesting approach in the theory of contractive mappings was recently given by Samet et al. (Nonlinear Anal. 75, 2012, 2154-2165) by using the concept of α-ψ contractive type mappings in metric spaces. The purpose of this paper is to give the generalized version of α-ψ contractive type mappings in complex valued metric spaces. For this, we define the notion of (α, φ)-contractive mappings of rational type and obtain fixed point theorems for such mappings in the framework of complex valued metric spaces. This extends and subsumes the recent results of Azam et al. (Numerical Functional Analysis and optimization 32, 2011, 243-253) and Rouzkard and Imdad (Computers and Mathematics with Applications 2012, doi:10.1016/j.camwa.2012.02.063) regarding common fixed point theorems in complex valued metric spaces. Also, we derive common coupled fixed point theorems in complete complex valued metric spaces. Our results generalize many previously obtained results. Some examples are presen...
In this paper, some estimates for Dirichlet kernel has been proved. Also, we have obtained the co... more In this paper, some estimates for Dirichlet kernel has been proved. Also, we have obtained the complex form of modified trigonometric cosine and sine sums of X.Z. Krasniqi (10) and have proved the convergence of complex trigonometric series under class J* of complex coefficients in metric space j j j n jx a a x x n i n n n n t n i n t n i n n n e c c n e c c n e c e c e c e c
In the present paper, the concept of contraction has been extended in a refined manner by introdu... more In the present paper, the concept of contraction has been extended in a refined manner by introducing mathfrakD\mathfrak{D}mathfrakD-Contraction defined on a family mathfrakF\mathfrak{F}mathfrakF of bounded functions. Also, a new notion of fixed function has been introduced for a metric space. Some fixed function theorems along with illustrative examples have also been given to verify the effectiveness of our results. In addition, an application to medical science has also been presented. This application is based on best approximation of treatment plan for tumor patients getting intensity modulated radiation therapy(IMRT). In this technique, a proper DDC matrix truncation has been used that significantly improves accuracy of results. In 2013, Z. Tian \textit{et al.} presented a fluence map optimization(FMO) model for dose calculation by splitting the DDC matrix into two components on the basis of a threshold intensity value. Following this concept, a sequence of functions can be constructed through the presented ...
The present dissertation entitled, “A Study of New Topologies on R” comprises certain investigati... more The present dissertation entitled, “A Study of New Topologies on R” comprises certain investigations carried out by me at School of Mathematics, Thapar University, Patiala, under the supervision of Dr. Jatinderdeep Kaur, Assistant Professor, School of Mathematics, Thapar University, Patiala. The aim of this work is to find new topologies with this new set of basis B− and B+. The topologies generated from this new set of basis are different from standard, lower limit, upper limit and k-topologies. We compared well known topologies with new topologies on R. The whole work is divided into four chapters. Chapter 1 is introduction which includes brief account of definitions and their examples which will be required for the later chapters. In chapter 2, we have studied some main theorems which guarantees how topology can be generated from given base and vice-versa. The aim of chapter 3 is to study well known topologies on R and their topological properties. In chapter 4, we introduced new...
The present dissertation entitled, “Integrability and L−convergence of Certain Trigonometric Seri... more The present dissertation entitled, “Integrability and L−convergence of Certain Trigonometric Series”, contains a brief account of investigations carried out by me on L−convergence of Trigonometric Cosine Series under the supervision of Dr. Jatinderdeep Kaur, Assistant Professor, School of Mathematics and Computer Applications, Thapar University, Patiala. The work presented in this dissertation has been divided into four chapters. The first chapter is introductory. In this chapter, apart from setting up the notations and terminology to be used in sequel, we have presented some known results. The purpose of chapter II is to study the integrability and L−convergence of Fourier cosine series. In chapter III, we studied the necessary and sufficient condition for the L−convergence of Rees-Stanojevic cosine sums. In chapter IV, we have studied the L−convergence of Ram-Kumari modified cosine sum. Towards the end, references of various publications cited in the present dissertation have been...
In this paper, the results of Kano from one dimensional cosine and sine series are extended to tw... more In this paper, the results of Kano from one dimensional cosine and sine series are extended to two dimensional cosine and sine series. To extend these results, some classes of coefficient sequences such as class of semi convexity and class R are extended from one dimension to two dimensions. Further, the function f(x, y) is two dimensional Fourier Cosine and Sine series or equivalently it represents an integrable function or not, has been studied. Moreover, some results are obtained which are generalization of Moricz’s results. Keywords—Conjugate Dirichlet kernel, conjugate Fejer kernel, Fourier series, Semi-convexity.
Applied General Topology, 2014
The notion of coupled fixed point was introduced by Guo and Laksmikantham [12]. Later Gnana Bhask... more The notion of coupled fixed point was introduced by Guo and Laksmikantham [12]. Later Gnana Bhaskar and Lakshmikantham in [11] investigated the coupled fixed points in the setting of partially ordered set by defining the notion of mixed monotone property. Very recently, the concept of tripled fixed point was introduced by Berinde and Borcut [7]. Following this trend, Karapınar[19] defined the quadruple fixed point. In this manuscript, quadruple fixed point is discussed and some new fixed point theorems are obtained on partial metric spaces.
In this paper, we extend the result of Ram (3) and also study the L 1 - convergence of the r th d... more In this paper, we extend the result of Ram (3) and also study the L 1 - convergence of the r th derivative of cosine series.