Strong convergence theorems for a common fixed point of a finite family of multivalued mappings in certain Banach spaces

Abstract

In this paper, we introduce an new iterative algorithm for finding an element of the set of common fixed points for a fanite familiy of multivalued k-strictly pseudo contractive mappings in q-uniformly smooth real Banach spaces. Further, we prove strong convergence theorems of the iterative sequence generated by the proposed algorithm under suitable conditions. Our results extend and improve some important recent results.

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

“…With this definition at hand, many mathematicians proved some strong convergence theorems for approximating fixed points of multivalued k-strictly pseudo-contrcative mappings under some compactness conditions (see, for example, Sene et al [30], Chidume et .al [10], Sow et al [34] ).…”

Modified Viscosity Iterative Algorithm for Solving Variational Inclusion and Fixed Point Problems in Real Hilbert Space

“…By investigating the properties and behavior of fixed points in multivalued mappings, mathematicians have gained a deeper understanding of these fields and have been able to establish connections and develop new techniques. (See, [30], [10,11], [2], [7], [33], [9] and [26]).…”