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

Year 2020, , 100 - 111, 30.06.2020

Thierno Sow

https://doi.org/10.31197/atnaa.655466

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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