Search results for "contractive mapping"
showing 6 items of 16 documents
Some Common Fixed Point Results in Cone Metric Spaces
2009
We prove a result on points of coincidence and common fixed points for three self-mappings satisfying generalized contractive type conditions in cone metric spaces. We deduce some results on common fixed points for two self-mappings satisfying contractive type conditions in cone metric spaces. These results generalize some well-known recent results.
Fixed point results for $G^m$-Meir-Keeler contractive and $G$-$(\alpha,\psi)$-Meir-Keeler contractive mappings
2013
In this paper, first we introduce the notion of a $G^m$-Meir-Keeler contractive mapping and establish some fixed point theorems for the $G^m$-Meir-Keeler contractive mapping in the setting of $G$-metric spaces. Further, we introduce the notion of a $G_c^m$-Meir-Keeler contractive mapping in the setting of $G$-cone metric spaces and obtain a fixed point result. Later, we introduce the notion of a $G$-$(\alpha,\psi)$-Meir-Keeler contractive mapping and prove some fixed point theorems for this class of mappings in the setting of $G$-metric spaces.
On k-ball contractive retractions in F-normed ideal spaces
2010
Let X be an infinite dimensional F-normed space and r a positive number such that the closed ball B_r(X) of radius r is properly contained in X. For a bounded subset A of X, the Hausdorff measure of noncompactness gamma(A) of A is the infimum of all $\eps >0$ such that A has a finite $\eps$-net in X. A retraction R of B_r(X) onto its boundary is called k-ball contractive if $\gamma(RA) \le k \gamma(A)$ for each subset A of B_r(X). The main aim of this talk is to give examples of regular F-normed ideal spaces in which there is a 1-ball contractive retraction or, for any $\eps>0$, a $(1+ \eps)$-ball contractive retraction with positive lower Hausdorff measure of noncompactness.
A fixed point theorem for uniformly locally contractive mappings in a C-chainable cone rectangular metric space
2011
Recently, Azam, Arshad and Beg [ Banach contraction principle on cone rectangular metric spaces, Appl. Anal. Discrete Math. 2009] introduced the notion of cone rectangular metric spaces by replacing the triangular inequality of a cone metric space by a rectangular inequality. In this paper, we introduce the notion of c-chainable cone rectangular metric space and we establish a fixed point theorem for uniformly locally contractive mappings in such spaces. An example is given to illustrate our obtained result.
Fixed point theorems for twisted (α,β)-ψ-contractive type mappings and applications
2013
The purpose of this paper is to discuss the existence and uniqueness of fixed points for new classes of mappings defined on a complete metric space. The obtained results generalize some recent theorems in the literature. Several applications and interesting consequences of our theorems are also given.
On modified α-ϕ-fuzzy contractive mappings and an application to integral equations
2016
Abstract We introduce the notion of a modified α-ϕ-fuzzy contractive mapping and prove some results in fuzzy metric spaces for such kind of mappings. The theorems presented provide a generalization of some interesting results in the literature. Two examples and an application to integral equations are given to illustrate the usability of our theory.