An iterative algorithm on fixed points of relaxed Lipschitz operators

Ram U Verma

doi:10.1155/s1048953397000221

Abstract

Fixed points of Lipschitzian relaxed Lipschitz operators based on a generalized iterative algorithm are approximated.

Highlights

Wittman [6, Theorem 2], using an iterative procedure xn (1 an)X0 q- anTxn 1 for n _> 1, (1)approximated fixed points of nonexpansive mappings T:K-,K from a nonempty closed convex subset K of a real Hilbert space H into itself, where x0 is an element of g and {an} is an increasing sequence in [0, 1) such thatE nliman 1 and (1 an) oo. (2) n=lThis result refines a number of results including [1].Here our aim is to approximate the fixed points of Lipschitzian relaxed Lipschitz operators in a Hilbert space setting
Fixed points of Lipschitzian relaxed Lipschitz operators based on a generalized iterative algorithm are approximated
Approximated fixed points of nonexpansive mappings T:K-,K from a nonempty closed convex subset K of a real Hilbert space H into itself, where x0 is an element of g and {an} is an increasing sequence in [0, 1) such that

Summary

Introduction

Fixed points of Lipschitzian relaxed Lipschitz operators based on a generalized iterative algorithm are approximated. Wittman [6, Theorem 2], using an iterative procedure xn (1 an)X0 q- anTxn 1 for n _> 1, (1) Approximated fixed points of nonexpansive mappings T:K--,K from a nonempty closed convex subset K of a real Hilbert space H into itself, where x0 is an element of g and {an} is an increasing sequence in [0, 1) such that Our aim is to approximate the fixed points of Lipschitzian relaxed Lipschitz operators in a Hilbert space setting.

Objectives

Results

Conclusion