Abstract
We introduce a new general system of generalized nonlinear mixed composite-type equilibria and propose a new iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a general system of generalized nonlinear mixed composite-type equilibria, and the set of fixed points of a countable family of strict pseudocontraction mappings. Furthermore, we prove the strong convergence theorem of the purposed iterative scheme in a real Hilbert space. As applications, we apply our results to solve a certain minimization problem related to a strongly positive bounded linear operator. Finally, we also give a numerical example which supports our results. The results obtained in this paper extend the recent ones announced by many others.
Highlights
Let H be a real Hilbert space whose inner product and norm are denoted by ·, · and ·, respectively
Let C be a nonempty closed and convex subset of a real Hilbert space H
Motivated and inspired by the works in the literature, we introduce a new general system of generalized nonlinear mixed composite-type equilibria 1.12 and propose a new iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem, a general system of generalized nonlinear mixed composite-type equilibria, and the set of fixed points of a countable family of strict pseudocontraction mappings
Summary
Let H be a real Hilbert space whose inner product and norm are denoted by ·, · and · , respectively. Ceng and Yao 21 introduced and considered a relaxed extragradient-like method for finding a common element of the set of solutions of a system of generalized equilibria, the set of fixed points of a strictly pseudocontractive mapping, and the set of solutions of a equilibrium problem in a real Hilbert space and obtained a strong convergence theorem. Takahashi 10 , Ceng et al , Peng and Yao , and Yao et al. Motivated and inspired by the works in the literature, we introduce a new general system of generalized nonlinear mixed composite-type equilibria 1.12 and propose a new iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem, a general system of generalized nonlinear mixed composite-type equilibria, and the set of fixed points of a countable family of strict pseudocontraction mappings. The results presented in this paper extend the recent results of Cho et al 1 , Ceng and Yao 21 , Ceng et al 20 , and many authors
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