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Iterative methods for a generalized equilibrium problem and a nonexpansive multi-valued mapping. (English) Zbl 06779857

Summary: In this paper, we introduce new iterative schemes for approximating common elements of the set of solutions of generalized equilibrium problems and the set of fixed points of nonexpansive multi-valued mappings. We prove some strong convergence theorems of the sequences generated by our iterative process under appropriate additional assumptions in Hilbert spaces. Moreover, we give some numerical results for supporting our main theorem. Our main results improve the corresponding ones obtained in (S. Takahashi, W. Takahashi: Nonlinear Anal. 69: 1025-1033, 2008).

MSC:

47H04 Set-valued operators
47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
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