Journal of the Iranian Mathematical Society

Journal of the Iranian Mathematical Society

Theta method to approximate fixed points of nonexpansive multimaps in Banach spaces

Document Type : Research Article

Authors
1 Laboratory of Mathematical Analysis and Applications, Faculty of‎ ‎Technology, University‎ ‎of Hassiba Benbouali, Chlef‎, ‎Algeria.
2 Laboratory of Mathematical Analysis and Applications, University Oran 1‎, ‎Ahmed Ben Bella‎, ‎El M'naoeur‎, ‎BP 1524, Oran‎, ‎Algeria.
Abstract
In this paper‎, ‎we introduce a novel iterative scheme that integrates the Mann iteration process with the implicit $\theta$-method to approximate fixed points of nonexpansive multivalued mappings in Banach spaces‎. ‎Under suitable assumptions‎, ‎we establish both weak and strong convergence results for the proposed algorithm‎. ‎Furthermore‎, ‎we demonstrate the applicability of our method to variational inclusion problems and convex optimization problems‎. ‎A numerical example is presented to illustrate the efficiency and effectiveness of the approach‎.
Keywords
Subjects

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