Common Fixed Points of Three Multivalued Nonexpansive Random Operators For One Step Iterative Scheme

Authors

Sabah Hassan Malih Department of Mathematics, College of Education for Pure Science Ibn- ALHaitham, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0002-1600-3631
Wisam Mohammed Mukhlif Department of Mathematics, College of Education for pure science Ibn- ALHaitham, University of Baghdad, Baghdad, Iraq https://orcid.org/0009-0009-8635-2210
Shrooq Bahjat Smeein Information Department, Section Mathematics, Sultanate of Oman https://orcid.org/0009-0002-9351-4176

DOI:

https://doi.org/10.30526/37.2.3486

Keywords:

common fixed points, random operators,one-step iteration, Banach spaces

Abstract

In this paper, we introduce a new one-step iteration process in Banach space and prove the existence of a common random fixed point of three non-expansive multivalued random operators through strong and weak convergences of an iterative process. The necessary and sufficient condition for the convergence of a sequence of measurable functions to a random fixed point of non-expansive multivalued random operators in uniformly convex Banach spaces is also established. Our random iteration scheme includes new random multivalued iterations as special cases. The results obtained in this paper are an extension and refinement of previously known results. A new random iterative scheme for approximating random common fixed points of three random non-expansive multivalued random operators is defined and we have proved weak and strong convergence theorems in a uniformly convex Banach space.

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