Author
Farshid Khojasteh
Other affiliations: Islamic Azad University
Bio: Farshid Khojasteh is an academic researcher from Islamic Azad University, Arak. The author has contributed to research in topics: Metric space & Fixed-point theorem. The author has an hindex of 12, co-authored 41 publications receiving 519 citations. Previous affiliations of Farshid Khojasteh include Islamic Azad University.
Papers
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TL;DR: In this article, the authors introduced the simulation function and the notion of Z-contraction with respect to which generalize the Banach contraction principle and unify several known types of contractions involving the combination of d(Tx; Ty) and d(x; y): the related fixed point theorems are also proved.
Abstract: Let (X; d) be a metric space and T : X! X be a mapping. In this work, we introduce the mapping : (0;1) (0;1)! R, called the simulation function and the notion ofZ-contraction with respect to which generalize the Banach contraction principle and unify several known types of contractions involving the combination of d(Tx; Ty) and d(x; y): The related fixed point theorems are also proved.
202 citations
TL;DR: In this paper, the existence and uniqueness of a fixed point of an operator via simultaneous functions in the setting of complete quasi-metric spaces was investigated, and the results generalize and improve several recent results in literature.
Abstract: We investigate the existence and uniqueness of a fixed point of an operator via simultaneous functions in the setting of complete quasi-metric spaces. Our results generalize and improve several recent results in literature.
44 citations
TL;DR: In this article, the existence of the best proximity points of certain mapping defined via simulation functions in the frame of complete metric spaces is investigated and the uniqueness criteria for such mappings are considered.
Abstract: In this paper, we investigate of the existence of the best proximity points of certain mapping defined via simulation functions in the frame of complete metric spaces. We consider the uniqueness criteria for such mappings. The obtained results unify a number of the existing results on the topic in the literature.
43 citations
TL;DR: In this article, the authors show that a generalized weak contraction mapping has a unique endpoint if and only if it has the approximate endpoint property (i.e., the distance from the target to the target is constant).
Abstract: Let ( X , d ) be a complete metric space, and let T : X → P cl , bd ( X ) be a multi-valued generalized weak contraction mapping. Then T has a unique endpoint if and only if T has the approximate endpoint property. Our results extend previous results given by Ciric (1971) [15] , Nadler (1969) [11] , Daffer and Kaneko (1995) [9] and Amini-Harandi (2010) [8] .
33 citations
TL;DR: In this paper, the concept of manageable functions is introduced and some new existence theorems related to approximate fixed point property for manageable functions and -admissible multivalued maps are presented.
Abstract: We first introduce the concept of manageable functions and then prove some new existence theorems related to approximate fixed point property for manageable functions and -admissible multivalued maps. As applications of our results, some new fixed point theorems which generalize and improve Du's fixed point theorem, Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, and Nadler's fixed point theorem and some well-known results in the literature are given.
27 citations
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01 Jan 1985
TL;DR: The first group of results in fixed point theory were derived from Banach's fixed point theorem as discussed by the authors, which is a nice result since it contains only one simple condition on the map F, since it is easy to prove and since it nevertheless allows a variety of applications.
Abstract: Formally we have arrived at the middle of the book. So you may need a pause for recovering, a pause which we want to fill up by some fixed point theorems supplementing those which you already met or which you will meet in later chapters. The first group of results centres around Banach’s fixed point theorem. The latter is certainly a nice result since it contains only one simple condition on the map F, since it is so easy to prove and since it nevertheless allows a variety of applications. Therefore it is not astonishing that many mathematicians have been attracted by the question to which extent the conditions on F and the space Ω can be changed so that one still gets the existence of a unique or of at least one fixed point. The number of results produced this way is still finite, but of a statistical magnitude, suggesting at a first glance that only a random sample can be covered by a chapter or even a book of the present size. Fortunately (or unfortunately?) most of the modifications have not found applications up to now, so that there is no reason to write a cookery book about conditions but to write at least a short outline of some ideas indicating that this field can be as interesting as other chapters. A systematic account of more recent ideas and examples in fixed point theory should however be written by one of the true experts. Strange as it is, such a book does not seem to exist though so many people are puzzling out so many results.
994 citations
TL;DR: In this paper, the authors show that all fixed point results in cone metric spaces obtained recently, in which the assumption that the underlying cone is normal and solid is present, can be reduced to the corresponding results in metric spaces.
Abstract: Using an old M. Krein’s result and a result concerning symmetric spaces from [S. Radenovic, Z. Kadelburg, Quasi-contractions on symmetric and cone symmetric spaces, Banach J. Math. Anal. 5 (1) (2011), 38–50], we show in a very short way that all fixed point results in cone metric spaces obtained recently, in which the assumption that the underlying cone is normal and solid is present, can be reduced to the corresponding results in metric spaces. On the other hand, when we deal with non-normal solid cones, this is not possible. In the recent paper [M.A. Khamsi, Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl. 2010, 7 pages, Article ID 315398, doi:10.1115/2010/315398 ] the author claims that most of the cone fixed point results are merely copies of the classical ones and that any extension of known fixed point results to cone metric spaces is redundant; also that underlying Banach space and the associated cone subset are not necessary. In fact, Khamsi’s approach includes a small class of results and is very limited since it requires only normal cones, so that all results with non-normal cones (which are proper extensions of the corresponding results for metric spaces) cannot be dealt with by his approach.
233 citations
TL;DR: In this article, the authors introduced the simulation function and the notion of Z-contraction with respect to which generalize the Banach contraction principle and unify several known types of contractions involving the combination of d(Tx; Ty) and d(x; y): the related fixed point theorems are also proved.
Abstract: Let (X; d) be a metric space and T : X! X be a mapping. In this work, we introduce the mapping : (0;1) (0;1)! R, called the simulation function and the notion ofZ-contraction with respect to which generalize the Banach contraction principle and unify several known types of contractions involving the combination of d(Tx; Ty) and d(x; y): The related fixed point theorems are also proved.
202 citations
TL;DR: This paper slightly modify Khojasteh et?al.'s notion of simulation function and investigates the existence and uniqueness of coincidence points of two nonlinear operators using this kind of control functions.
140 citations