SOME REMARKS ABOUT UNIFORMLY LIPSCHITZIAN MAPPINGS AND LIPSCHITZIAN RETRACTIONS

On Uniformly Generalized Lipschitzian Mappings

We consider another class of generalized Lipschitzian type mappings and utilize the same to prove fixed point theorems for asymptotically regular and uniformly generalized Lipschitzian one-parameter semigroups of self-mappings defined on bounded metric spaces equipped with uniform normal structure which yield corresponding results in respect of semigroup of iterates of a self-mapping as corolla...

Convergence theorems for uniformly quasi-Lipschitzian mappings

Remarks on Lipschitzian Mappings and Some Fixed Point Theorems

Let X, Y be the normed spaces, C ⊂ X a convex set, and T : C → Y a continuous mapping. Some weak conditions implying the Lipschitz continuity of T are presented. Applications to the fixed point theory and theory of composition operators are presented.

Fixed 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.

Fixed Points of Uniformly Lipschitzian Mappings in Metric Spaces

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 lipsc...