Fixed Points of Uniformly Lipschitzian Mappings in Metric Spaces
نویسندگان
چکیده
Two fixed point theorems for uniformly lipschitzian mappings in metric spaces, due respectively to E. Lif̌sic and to T.-C. Lim and H.-K. Xu, are compared within the framework of the so-called CAT(0) spaces. It is shown that both results apply in this setting, and that Lif̌sic’s theorem gives a sharper result. Also, a new property is introduced that yields a fixed point theorem for uniformly lipschitzian mappings in a class of hyperconvex spaces, a class which includes those possessing property (P ) of Lim and Xu.
منابع مشابه
Strong convergence results for fixed points of nearly weak uniformly L-Lipschitzian mappings of I-Dominated mappings
In this paper, we prove strong convergence results for a modified Mann iterative process for a new class of I- nearly weak uniformly L-Lipschitzian mappings in a real Banach space. The class of I-nearly weak uniformly L-Lipschitzian mappings is an interesting generalization of the class of nearly weak uniformly L-Lipschitzian mappings which inturn is a generalization of the class of nearly unif...
متن کاملApproximating Common Fixed Points of Two Sequences of Uniformly Quasi-lipschitzian Mappings in Convex Cone Metric Spaces
A convex cone metric space is a cone metric space with a convex structure. In this paper, we extend an Ishikawa type iterative scheme with errors to approximate a common fixed point of two sequences of uniformly quasi-Lipschitzian mappings to convex cone metric spaces. Our result generalizes Theorem 2 in [1].
متن کاملOn The Convergence Of Modified Noor Iteration For Nearly Lipschitzian Maps In Real Banach Spaces
In this paper, we obtained the convergence of modified Noor iterative scheme for nearly Lipschitzian maps in real Banach spaces. Our results contribute to the literature in this area of re- search.
متن کاملFixed Points of Uniformly Lipschitzian Mappings in Metric Trees
In this paper we examine the basic structure of metric trees and prove fixed point theorems for uniformly Lipschitzian mappings in metric trees.
متن کاملFixed points for total asymptotically nonexpansive mappings in a new version of bead space
The notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $CAT(0)$ space, where the curvature is bounded from above by zero. In fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. In this paper, w...
متن کامل