A New Hybrid Iterative Method for Solving Fixed Points Problems for a Finite Family of Multivalued Strictly Pseudo-Contractive Mappings and Convex Minimization Problems in Real Hilbert Spaces

Year 2021, Volume: 9 Issue: 3, 95 - 107, 30.09.2021

Thierno Sow

https://doi.org/10.36753/mathenot.592227

Abstract

In the present work, we introduce a new hybrid iterative  process  which is a combination of proximal point algorithms and a modified Krasnoselskii-Mann algorithm for approximating a common element of the set of minimizers of a convex function and the set of common fixed points of a finite family of multivalued strictly pseudo-contractive mappings in the framework of Hilbert spaces. We then prove strong convergence of the proposed iterative process without imposing any compactness condition on the mapping or the space. The results we obtain extend and improve some recent known results.

Keywords

Fixed points problems, Convex minimization problem, Set-valued operators, Iterative methods

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