Theta method to approximate fixed points of nonexpansive multimaps in Banach spaces
نویسندگان
1 Laboratory of Mathematical Analysis and Applications, University Oran 1, Ahmed Ben Bella, El M'naoeur, BP 1524, Oran, Algeria.
2 Laboratory of Mathematical Analysis and Applications, Faculty of Technology, University of Hassiba Benbouali, Chlef, Algeria.
doi
10.30504/jims.2025.468166.1195چکیده
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.
