Search results for "coincidence point"
showing 10 items of 64 documents
Fixed point theory for 1-set contractive and pseudocontractive mappings
2013
The purpose of this paper is to study the existence and uniqueness of fixed point for a class of nonlinear mappings defined on a real Banach space, which, among others, contains the class of separate contractive mappings, as well as to see that an important class of 1-set contractions and of pseudocontractions falls into this type of nonlinear mappings. As a particular case, we give an iterative method to approach the fixed point of a nonexpansive mapping. Later on, we establish some fixed point results of Krasnoselskii type for the sum of two nonlinear mappings where one of them is either a 1-set contraction or a pseudocontraction and the another one is completely continuous, which extend …
Common fixed points for discontinuous mappings in fuzzy metric spaces
2008
In this paper we prove some common fixed point theorems for fuzzy contraction respect to a mapping, which satisfies a condition of weak compatibility. We deduce also fixed point results for fuzzy contractive mappings in the sense of Gregori and Sapena.
A common fixed point theorem for two weakly compatible pairs in G-metric spaces using the property E.A
2013
In view of the fact that the fixed point theory provides an efficient tool in many fields of pure and applied sciences, we use the notion of the property E.A to prove a common fixed point theorem for weakly compatible mappings. The presented results are applied to obtain the solution of an integral equation and the bounded solution of a functional equation arising in dynamic programming.
Further generalization of fixed point theorems in Menger PM-spaces
2015
In this work, we establish some fixed point theorems by revisiting the notion of ψ-contractive mapping in Menger PM-spaces. One of our results (namely, Theorem 2.3) may be viewed as a possible answer to the problem of existence of a fixed point for generalized type contractive mappings in M-complete Menger PM-spaces under arbitrary t-norm. Some examples are furnished to demonstrate the validity of the obtained results.
A homotopy fixed point theorem in 0-complete partial metric space
2015
We generalize a result of Feng and Liu, on multi-valued contractive mappings, for studying the relationship between fixed point sets and homotopy fixed point sets. The presented results are discussed in the generalized setting of 0-complete partial metric spaces. An example and a nonlinear alternative of Leray-Schauder type are given to support our theorems.
Common fixed points for self-mappings on partial metric spaces
2012
Abstract In this paper, we prove some results of a common fixed point for two self-mappings on partial metric spaces. Our results generalize some interesting results of Ilić et al. (Appl. Math. Lett. 24:1326-1330, 2011). We conclude with a result of the existence of a fixed point for set-valued mappings in the context of 0-complete partial metric spaces. MSC:54H25, 47H10.
On a pair of fuzzy $\varphi$-contractive mappings
2010
We establish common fixed point theorems for fuzzy mappings under a $\varphi$-contraction condition on a metric space with the d_$\infty$-metric (induced by the Hausdorff metric) on the family of fuzzy sets. The study of fixed points of fuzzy set-valued mappings related to the d_$\infty$-metric is useful in geometric problems arising in high energy physics. Our results generalize some recent results.
Unified Metrical Common Fixed Point Theorems in 2-Metric Spaces via an Implicit Relation
2013
We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results. Moreover, we study the existence of solutions of a nonlinear integral equation.
A fixed point theorem inG-metric spaces viaα-series
2014
In the context of G -metric spaces we prove a common fixed point theorem for a sequence of self mappings using a new concept of α-series. Keywords: α-series, common fixed point, G -metric space Quaestiones Mathematicae 37(2014), 429-434
Fixed point properties and proximinality in Banach spaces
2009
Abstract In this paper we prove the existence of a fixed point for several classes of mappings (mappings admitting a center, nonexpansive mappings, asymptotically nonexpansive mappings) defined on the closed convex subsets of a Banach space satisfying some proximinality conditions. In particular, we derive a sufficient condition, more general than weak star compactness, such that if C is a bounded closed convex subset of l 1 satisfying this condition, then every nonexpansive mapping T : C → C has a fixed point.