Common Attractive Point Theorems for a Finite Family of Multivalued Nonexpansive Mappings in Banach Spaces

Year 2022, Volume: 5 Issue: 3, 372 - 386, 30.09.2022

Atit Wiriyapongsanon Warunun Inthakon Narawadee Phudolsitthiphat

https://doi.org/10.53006/rna.1128729

Abstract

OurmainpurposeofthispaperistointroducethemodifiedMannandIshikawaiteratesforfindingacommonattractive
point of a finite family of multivalued nonexpansive mappings in the setting of uniformly convex Banach spaces. We
obtain necessary and sufficient conditions to guarantee the strong convergence of the proposed algorithms without
closedness of the domain of such mappings. Moreover, we derive some consequences from our main result to fixed
point result of such mappings. Finally, the numerical results are provided to support our main theorem.

Keywords

common attractive point, multivalued nonexpansive mapping, uniformly convex Banach space, demicompact

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