Fixed point theorems for uniformly Lipschitzian semigroups in uniformly convex spaces

Fixed Point Theorems in Uniformly Convex Banach Spaces

The notion of an asymptotic center is used to prove a number of results concerning the existence of fixed points under certain selfmappings of a closed and bounded convex subset of a uniformly convex Banach space.

Fixed Point Theorems for Generalized Lipschitzian Semigroups in Banach Spaces

Fixed point theorems for generalized Lipschitzian semigroups are proved in puniformly convex Banach spaces and in uniformly convex Banach spaces. As applications, its corollaries are given in a Hilbert space, in Lp spaces, in Hardy space Hp , and in Sobolev spaces Hk,p , for 1<p <∞ and k≥ 0.

Fixed Point Theorems for Generalized Lipschitzian Semigroups

Let K be a nonempty subset of a p-uniformly convex Banach space E, G a left reversible semitopological semigroup, and = {Tt : t ∈G} a generalized Lipschitzian semigroup of K into itself, that is, for s ∈ G, ‖Tsx−Tsy‖ ≤ as‖x−y‖+bs(‖x−Tsx‖+ ‖y−Tsy‖)+cs(‖x−Tsy‖+‖y−Tsx‖), for x,y ∈ K where as,bs ,cs > 0 such that there exists a t1 ∈ G such that bs +cs < 1 for all s t1. It is proved that if there ex...

Fixed Point Theorems for a Semigroup of Total Asymptotically Nonexpansive Mappings in Uniformly Convex Banach Spaces

In this paper, we provide existence and convergence theorems of common fixed points for left (or right) reversible semitopological semigroups of total asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper extend and improve some recent results announced by other authors.

Convergence theorems for uniformly quasi-Lipschitzian mappings