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Fixed point theorems for generalized weakly contractive mappings
Ramendra Krishna Bose,Mrinal Kanti Roychowdhury
Surveys in Mathematics and its Applications , 2009,
Abstract: In this paper several fixed point theorems for generalized weakly contractive mappings in a metric space setting are proved. The set of generalized weakly contractive mappings considered in this paper contains the family of weakly contractive mappings as a proper subset. Fixed point theorems for single and multi-valued mappings, approximating scheme for common fixed point for some mappings, and fixed point theorems for fuzzy mappings are presented. It extends the work of several authors including Bose and Roychowdhury.
Fixed point theorems of soft contractive mappings  [PDF]
Murat I. Yazar,Cigdem Gunduz,Sadi Bayramov
Mathematics , 2013,
Abstract: The first aim of this paper is to examine some important properties of soft metric spaces. Second is to introduce soft continuous mappings and investigate properties of soft continuous mappings. Third is to prove some fixed point theorems of soft contractive mappings on soft metric spaces.
Convergence Theorems of an Implicit Iterates with Errors for Total Asymptotically Pseudo-Contractive Mappings
G.S. Saluja
International Journal of Analysis and Applications , 2013,
Abstract: The goal of this paper is to establish weak and strong convergence theorems of an implicit iteration process with errors to converge to common fixed points for a finite family of uniformly $L$-Lipschitzian total asymptotically pseudo-contractive mappings in the framework of Banach spaces. Our results extend the corresponding result of [2.5.8.10] and many others.
Generalized - Contractive Type Mappings and Related Fixed Point Theorems with Applications
Erdal Karap nar,Bessem Samet
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/793486
Abstract: We establish fixed point theorems for a new class of contractive mappings. As consequences of our main results, we obtain fixed point theorems on metric spaces endowed with a partial order and fixed point theorems for cyclic contractive mappings. Various examples are presented to illustrate our obtained results.
Common Fixed Point Theorems for - -Contractive Type Mappings  [PDF]
Jalal Hassanzadeasl
International Journal of Analysis , 2013, DOI: 10.1155/2013/654659
Abstract: Recently, Samet et al. (2012) introduced the notion of - -contractive type mappings. They established some fixed point theorems for these mappings in complete metric spaces. In this paper, we introduce the notion of a coupled - -contractive mapping and give a common fixed point result about the mapping. Also, we give a result of common fixed points of some coupled self-maps on complete metric spaces satisfying a contractive condition. 1. Introduction We know fixed point theory has many applications and was extended by several authors from different views (see, e.g., [1–33]). Recently, Samet et al. introduced the notion of - -contractive type mappings [3]. Denote with the family of nondecreasing functions such that for all , where is the th iterate of . It is known that for all and [3]. Let be a metric space, a self map on , and . Then, is called a - -contractive mapping whenever for all . Also, we say that is -admissible whenever implies for all [3]. Also, we say that has the property ( ) if is a sequence in such that for all and , then for all . Let be a complete metric space and let a -admissible - -contractive mapping on . Suppose that there exists such that . If is continuous or has the property ( ), then has a fixed point (see [3]; Theorems 2.1 and 2.2). Finally, we say that has the property ( ) whenever for each there exists such that and . If has the property ( ) in the Theorems??2.1 and 2.2, then has a unique fixed point ([3]; Theorem 2.3). It is considerable that the results of Samet et al. generalize similar ordered results in the literature (see the results of the third section [3]). The aim of this paper is introducing the notion of generalized coupled - -contractive mappings and give a common fixed point result about the mappings. Definition 1. Let?? ??the family of functions satisfy:(i) and for all ;(ii) is continuous;(iii) is nondecreasing on ;(iv) for all . Definition 2. Let the family of functions satisfy is nondecreasing; , for all . These functions are known in the literature as ( )-comparison functions. It is easily proved that if is a ( )-comparison function, then for all . Definition 3. Let be a metric space, and let with given coupled mappings. Let , , , and let for all coupled mappings and . One says that ,?? are generalized coupled -contractive mappings whenever for all . Definition 4. Let , and let . One says that ,?? are coupled -admissible if for all . Definition 5. Let be a compete metric space. For two subsets ,?? of , one marks , if for all , there exists such that . Definition 6. A partial metric on a nonempty set is a
Fixed Point Theorems and Asymptotically Regular Mappings in Partial Metric Spaces  [PDF]
Satish Shukla,Ishak Altun,Ravindra Sen
ISRN Computational Mathematics , 2013, DOI: 10.1155/2013/602579
Abstract: The notion of asymptotically regular mapping in partial metric spaces is introduced, and a fixed point result for the mappings of this class is proved. Examples show that there are cases when new results can be applied, while old ones (in metric space) cannot. Some common fixed point theorems for sequence of mappings in partial metric spaces are also proved which generalize and improve some known results in partial metric spaces. 1. Introduction Matthews [1] introduced partial metric spaces as a part of the study of denotational semantics of data flow networks. In partial metric space, the usual metric was replaced by partial metric, with a property that the self-distance of any point may not be zero. In fact, it is widely recognized that partial metric spaces play an important role in constructing models in the theory of computation. Partial metric has applications in the branches of science where the size of data point is represented by its self-distance. The fixed point of a contraction mapping in partial metric space has zero self-distance; that is, fixed point is a total object. Every metric space is a partial metric space with zero self-distance that is, partial metric spaces are the generalization of metric spaces. O’Neill [2] generalized the concept of partial metric space a bit further by admitting negative distances. The partial metric defined by O’Neill is called dualistic partial metric. Heckmann [3] generalized it by omitting small self-distance axiom. The partial metric defined by Heckmann is called weak partial metric. Banach contraction principle ensures the existence and uniqueness of a fixed point of a contractive self-map of metric space and has many applications in applied sciences. The fixed point result of Matthews is the generalization of the following Banach contraction principle. Let be a complete metric space and let be a self-map on . If there exists such that for all , then has a unique fixed point in . The fixed point result of Matthews is generalized by several authors for single self map in partial metric spaces (see, e.g., [4–6]). Almost all contractive conditions in these papers imply the asymptotic regularity of the mapping under consideration. The purpose of this paper is to prove some common fixed point theorems for a sequence of self maps on partial metric spaces and generalize the result of Matthews. The notion of asymptotically regular mapping in partial metric spaces is introduced and a fixed point result for the mappings of this class is also proved. 2. Definitions and Preliminaries First, we recall some
Fixed Point Theorems for -Contractive Mappings in Ordered Metric Spaces
Chi-Ming Chen
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/756453
Abstract: We obtain some new fixed point theorems for -contractive mappings in ordered metric spaces. Our results generalize or improve many recent fixed point theorems in the literature (e.g., Harjani et al., 2011 and 2010).
Some Fixed Point Theorems for Nonlinear Set-Valued Contractive Mappings
Zeqing Liu,Zhihua Wu,Shin Min Kang,Sunhong Lee
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/786061
Abstract: Four fixed point theorems for nonlinear set-valued contractive mappings in complete metric spaces are proved. The results presented in this paper are extensions of a few well-known fixed point theorems. Two examples are also provided to illustrate our results.
Common fixed point theorems of contractive-type mappings  [PDF]
Hee Soo Park,Jeong Sheok Ume
International Journal of Mathematics and Mathematical Sciences , 2004, DOI: 10.1155/s0161171204404608
Abstract: Using the concept of D-metric we prove some common fixed point theorems for generalized contractive mappings on a complete D-metric space. Our results extend, improve, and unify results of Fisher and Ćirić.
Common Fixed Point Theorems on Weakly Contractive and Nonexpansive Mappings  [cached]
Xiao Jian-Zhong,Zhu Xing-Hua
Fixed Point Theory and Applications , 2008,
Abstract: A family of commuting nonexpansive self-mappings, one of which is weakly contractive, are studied. Some convergence theorems are established for the iterations of types Krasnoselski-Mann, Kirk, and Ishikawa to approximate a common fixed point. The error estimates of these iterations are also given.
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