Ishikawa iteration convergence to fixed points of a multi-valued mapping in modular function spaces

Wondimu Woldie Kassu, Mengistu Goa Sangago

Abstract


We prove the ρ-convergence of Ishikawa iterative algorithm to fixed points of a multi-valued mapping T:C->Pρ(C), where C is a nonempty ρ-bounded ρ-closed subset of Lρ, ρ is a convex function modular satisfying ∆2-type condition, and Pρ(C) is the family of nonempty ρ-bounded ρ-proximinal subsets of C, such that the mapping PT is ρ-nonexpansive. This is the modular version of approximating fixed points of multi-valued nonexpansive mapping in Banach spaces by Ishikawa iterative algorithm and it generalizes some results in the literature.

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Published: 2024-05-21

How to Cite this Article:

Wondimu Woldie Kassu, Mengistu Goa Sangago, Ishikawa iteration convergence to fixed points of a multi-valued mapping in modular function spaces, Adv. Fixed Point Theory, 14 (2024), Article ID 22

Copyright © 2024 Wondimu Woldie Kassu, Mengistu Goa Sangago. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Advances in Fixed Point Theory

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