Nonlinear ergodic theorems for a semitopological semigroup of non-Lipschitzian mappings without convexity

Nonlinear Ergodic Theorems for a Semitopological Semigroup of Non-lipschitzian Mappings without Convexity

Let G be a semitopological semigroup, C a nonempty subset of a real Hilbert space H , and = {Tt : t ∈ G} a representation of G as asymptotically nonexpansive type mappings of C into itself. Let L(x)= {z ∈H : infs∈G supt∈G ‖Ttsx−z‖ = inf t∈G ‖Ttx−z‖} for each x ∈ C and L( )= ⋂x∈C L(x). In this paper, we prove that ⋂s∈G conv{Ttsx : t ∈ G}⋂L( ) is nonempty for each x ∈ C if and only if there exist...

Convergence theorems for uniformly quasi-Lipschitzian mappings

A Weak Ergodic Theorem for Infinite Products of Lipschitzian Mappings

Let K be a bounded, closed, and convex subset of a Banach space. For a Lipschitzian self-mapping A of K , we denote by Lip(A) its Lipschitz constant. In this paper, we establish a convergence property of infinite products of Lipschitzian self-mappings of K . We consider the set of all sequences {At}t=1 of such selfmappings with the property limsupt→∞ Lip(At) ≤ 1. Endowing it with an appropriate...

Convergence theorems for a countable family of Lipschitzian mappings

and Applied Analysis 3 where θn 1 − αn Ln − 1 diamC 2 → 0 as n → ∞ and prove that {xn} defined by 1.5 converges strongly to P∩n 1F Tn x. In this paper, we establish strong convergence theorems for finding common fixed points of a countable family of Lipschitzian mappings in a real Hilbert space. Moreover, we also apply our results for asymptotically nonexpansive mappings. 2. Preliminaries Let H...

Fixed-point Theorems for Multivalued Non-expansive Mappings without Uniform Convexity

Let X be a Banach space whose characteristic of noncompact convexity is less than 1 and satisfies the nonstrict Opial condition. Let C be a bounded closed convex subset of X , KC(C) the family of all compact convex subsets of C, and T a nonexpansive mapping from C into KC(C). We prove that T has a fixed point. The nonstrict Opial condition can be removed if, in addition, T is a 1-χcontractive m...