Abdalla Tallafha - Academia.edu (original) (raw)

Papers by Abdalla Tallafha

European Journal of Pure and Applied Mathematics

In an attempt to solve the farthest point problem, we introduce a new class of uniquely remotal s... more In an attempt to solve the farthest point problem, we introduce a new class of uniquely remotal sets. Namely, the class of uniquely distant sets. Then, we prove that in a separable Hilbert space, every uniquely distant set is a singleton.

Computers, materials & continua, 2020

Fixed point theory is one of the most important subjects in the setting of metric spaces since fi... more Fixed point theory is one of the most important subjects in the setting of metric spaces since fixed point theorems can be used to determine the existence and the uniqueness of solutions of such mathematical problems. It is known that many problems in applied sciences and engineering can be formulated as functional equations. Such equations can be transferred to fixed point theorems in an easy manner. Moreover, we use the fixed point theory to prove the existence and uniqueness of solutions of such integral and differential equations. Let X be a non-empty set. A fixed point for a self-mapping T on X is a point ∈ that satisfying T e=e. One of the most challenging problems in mathematics is to construct some iterations to faster the calculation or approximation of the fixed point of such problems. Some mathematicians constructed and generated some new iteration schemes to calculate or approximate the fixed point of such problems such as Mann et al. [Mann (1953); Ishikawa (1974); Sintunavarat and Pitea (2016); Berinde (2004b); Agarwal, O'Regan and Sahu (2007)]. The main purpose of the present paper is to introduce and construct a new iteration scheme to calculate or approximate the fixed point within a fewer number of steps as much as we can. We prove that our iteration scheme is faster than the iteration schemes given by Sintunavarat et al. [Sintunavarat and Pitea (2016); Agarwal, O'Regan and Sahu (2007); Mann (1953); Ishikawa (1974)]. We give some numerical examples by using MATLAB to compare the efficiency and effectiveness of our iterations scheme with the efficiency of Mann et al. [Mann (1953); Ishikawa (1974); Sintunavarat and Pitea (2016); Abbas and Nazir (2014); Agarwal, O'Regan and Sahu (2007)] schemes. Moreover, we introduce a problem raised from Newton's law of cooling as an application of our new iteration scheme. Also, we support our application with a numerical example and figures to illustrate the validity of our iterative scheme.

WSEAS transactions on mathematics, Feb 2, 2023

In this paper, we introduce two new classes of mappings called ρ − α − and ρ − α − k −nonspreadin... more In this paper, we introduce two new classes of mappings called ρ − α − and ρ − α − k −nonspreading mappings to broaden the idea of − attractive elements in modular function spaces (MFS). In the MFS that are put up, we also demonstrate several approximation results and existence results. Illustration examples are provided to clarify the results.

Nonlinear functional analysis and applications, Aug 28, 2021

In this paper we obtain a unique common fixed point theorem for four self-maps which are involved... more In this paper we obtain a unique common fixed point theorem for four self-maps which are involved in (φ, ψ)-weak contraction of a partially ordered b-metric space. The necessary condition has been given to a space for the existence of an unique common fixed of the maps. And our work changed conditions and nonlinear contraction, and search for the unique common fixed point of the maps.

The Basic Sciences Research Institute, Mar 1, 2020

Springer Proceedings in Mathematics & Statistics, 2016

In this paper, we shall define Lipschitz condition for functions and contraction functions on non... more In this paper, we shall define Lipschitz condition for functions and contraction functions on non-metrizable spaces. Finally, we ask the natural question: "Does every contraction have a unique fixed point?". 5.1 Introduction A uniform space is a set with a uniform structure. Uniform spaces are topological spaces with additional structure that is used to define uniform properties such as completeness, uniform continuity and uniform convergence. The notion of uniformity has been investigated by several mathematicians such as Weil [10-12], Cohen [3, 4] and Graves [6]. The theory of uniform spaces was given by Bourbaki in [2]. Also Weil's booklet [12] defines uniformly continuous mapping. Contraction functions on complete metric spaces played an important role in the theory of fixed point (Banach fixed point theory). Lipschitz condition and contractions are usually discussed in metric and normed spaces, and have never been studied in a non-metrizable space. The object of this paper is to define Lipschitz condition, and contraction mapping on semi-linear uniform spaces, which enables us to study fixed point for such functions. We believe that the structure of semilinear uniform spaces is very rich, and all the known results on fixed point theory can be generalized. Let X be a non-empty set and D X be a collection of all subsets of X X, such that each element V of D X contains the diagonal D f.x; x/ W x 2 Xgand V D V 1 D f.y; x/ W .x; y/ 2 Vg for all V 2 D X. D X is called the family of all entourages of the diagonal. Let be a sub-collection of D X. Then we have the following definition.

The Banach fixed point theory is one of the important results in pure mathematics that Banach pro... more The Banach fixed point theory is one of the important results in pure mathematics that Banach proved in 1922. This theory was expanded by several authors in different areas by introducing different contraction conditions. In this work, we extend the Banach fixed point theorem in modular metric spaces by investigating contractive conditions involving integral types. More precisely, we prove some existence and uniqueness theorems of a common fixed point of self mappings satisfying contraction conditions of the integral type. Then, we state some corollaries, and examples to illustrate the validity of our results.

Turkish Journal of Mathematics, 2000

In this paper we shall introduce the concept of being countable dense homogeneous bitopological s... more In this paper we shall introduce the concept of being countable dense homogeneous bitopological spaces and define several kinds of this concept. We shall give some results concerning these bitopological spaces and their relations. Also, we shall prove that all of these bitopological spaces satisfying the axioms p-T0 and p-T1 . AMS 1991 classification: 54E55, 54D10, 54G20.

Tallafha, A. andAlhihi, S. in [17], Defined m−contraction, and modefid semi-linear uniform space ... more Tallafha, A. andAlhihi, S. in [17], Defined m−contraction, and modefid semi-linear uniform space (X, ), and asked the following question. If f is an m−contraction from a complete modified semi-linear uniform space (X, ) to it self, is f has a unique fixed point. In this paper we shall answer partially the question given by Tallafha, A. and Alhihi, S. in [17] for 2−contraction, besides we shall give an intrested properties of modefied semi-linear uniform spaces. AMS subject classification: Primary 54E35, Secondary 41A65.

Dynamic Systems and Applications, 2020

Iranian Journal of Mathematical Sciences and Informatics, 2021

Tallafha, A. and Alhihi S. in [15], asked the following question. If f is a contraction from a co... more Tallafha, A. and Alhihi S. in [15], asked the following question. If f is a contraction from a complete semi-linear uniform space (X, Γ) to it self, is f has a unique fixed point. In this paper, we shall answer this question negatively and we shall show that convex metric space and Mspace are equivalent except uniqueness. Also, we shall characterize convex metric spaces and use this characterization to give some application using semi-linear uniform spaces

International Journal of Apllied Mathematics, 2021

In this paper, we employ the concept of C-class functions to prove some fixed point results in th... more In this paper, we employ the concept of C-class functions to prove some fixed point results in the setting of an extended b-metric space. Our result extend and generalize many existing results in the literature. Moreover, we introduce an example to show the validity of our results.

Computers, Materials & Continua, 2020

International Journal of Electrical and Computer Engineering (IJECE), 2020

In this Article, we introduce the notion of an ∈φ-contraction which based on modified ω-distance ... more In this Article, we introduce the notion of an ∈φ-contraction which based on modified ω-distance mappings and employ this new definition to prove some fixed point result. Moreover, we introduced an interesting example and an application to highlight the importance of our work.

Journal of Semigroup Theory and Applications, 2019

In this paper we shall obtaine a new results conserning fixed point in D ∗ Metric Spaces, besides... more In this paper we shall obtaine a new results conserning fixed point in D ∗ Metric Spaces, besides we correct the proves of some results obtaned by, T. Veerapandi and AJI. M Pillai in [35].

Axioms, 2019

In this manuscript, we utilize the concept of modified ω -distance mapping, which was introduced ... more In this manuscript, we utilize the concept of modified ω -distance mapping, which was introduced by Alegre and Marin [Alegre, C.; Marin, J. Modified ω -distance on quasi metric spaces and fixed point theorems on complete quasi metric spaces. Topol. Appl. 2016, 203, 120–129] in 2016 to introduce the notions of ( ω , φ ) -Suzuki contraction and generalized ( ω , φ ) -Suzuki contraction. We employ these notions to prove some fixed point results. Moreover, we introduce an example to show the novelty of our results. Furthermore, we introduce some applications for our results.

Mathematics, 2019

The ω -distance mapping is one of the important tools that can be used to get new contractions in... more The ω -distance mapping is one of the important tools that can be used to get new contractions in fixed point theory. The aim of this paper is to use the concept of modified ω -distance mapping to introduce the notion of rational ( α , β ) φ - m ω contraction. We utilize our new notion to construct and formulate many fixed point results for a pair of two mappings defined on a nonempty set A. Our results modify many existing known results. In addition, we support our work by an example.

Far East Journal of Mathematical Sciences (FJMS), 2017

A semi-linear uniform space is defined by Tallafha and Khalil in [13], wherein best approximation... more A semi-linear uniform space is defined by Tallafha and Khalil in [13], wherein best approximations have been investigated. In this paper, we survey the important properties of a semi-linear uniform space () Γ , X given in [1, 2, 11-17]. Also, we enumerate some open problems in approximation theory and fixed point theory in semi-linear uniform spaces. Finally, we settle an open question given in [12], in negation.

International Journal of Pure and Apllied Mathematics, 2016

Vector calculus is an important subject in mathematics with applications in all areas of applied ... more Vector calculus is an important subject in mathematics with applications in all areas of applied sciences. Till now researchers deal with the partial fractional derivative as the fractional derivative with respect to x, y,.... In this paper we shall define total and directional fractional derivative of functions of several variables, we set some basics about fractional vector calculus then we use our definition to modify the definition of conformal fractional derivative obtained by R. Khalil et al [6].