A PRODUCT TOPOLOGY AND STRONG CONVERGENCE SCHEME FOR FINDING COMMON FIXED POINTS OF A FAMILY OF NONEXPANSIVE SEMIGROUP

A PRODUCT TOPOLOGY AND STRONG CONVERGENCE SCHEME FOR FINDING COMMON FIXED POINTS OF A FAMILY OF NONEXPANSIVE SEMIGROUP

E. Soori, N. Abasi, A. Zafari, L. Hamidmanesh, M. Manavi

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Abstract

In this paper, we consider the product space EI with the product topology generated by the strong topologies on E for each i 2 I and using a family of nonexpan- sive semigroup in a product spaces EI , where E is a real strictly convex and re exive smooth Banach space and I is a nonempty set. And also, we introduce an algorithm in the product space EI consisting of all functions from I to E and prove the convergence theorem of the proposed algorithms.

Keywords

Product topology, Fixed point, Nonexpansive mapping, Representation, Sunny nonexpansive retraction.