Iterative algorithm for computing fixed points of demicontractive and zeros points of multivalued accretive operators in certain Banach spaces with application

Abstract

In this paper, an iterative algorithm for finding a common point of the set of common zero of an infinite family of multivalued accretive operators and the set of fixed points of a demicontractive operator is constructed and studied in certain Banach spaces having a weakly continuous duality map. Under suitable control conditions, strong convergence of the sequence generated by proposed algorithm to a common point of the two sets is established. Moreover, application to convex minimization problems involving an infinite family of lower semi-continuous and convex functions are included.The main theorems develop and complement the recent results announced by researchers in this area.

Keywords

• Proximal point algorithm,Demicontractive operators,Accretive operators,Weakly continuous duality maps

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