Hilbert 空间中不动点问题, 变分不等式系统和分裂均衡问题迭代算法的强收敛定理

Abstract

Abstract:

In this paper, we consider a common solution of three problems in real Hilbert spaces including the fixed points problem for asymptotically nonexpansive mapping, a system of variational inequalities and the split equilibrium problem. Under some suitable conditions imposed on the sequence of parameters, we prove that the sequence generated by the modified viscosity approximation method converges strongly to a common element of the solution set of these three kinds of problems. The results obtained in this article extend and improve the corresponding results of the relevant literature.

Key words: Asymptotically nonexpansive mapping, System of variational inequalities, Split equilibrium problem, Fixed point problem

CLC Number:

O177.91

Pan Lingrong, Wang Yuanheng. The Strong Convergence Theorem of Iterative Algorithms for the Fixed Point Problem, a System of Variational Inequalities, and a Split Equilibrium Problem in Hilbert Spaces[J].Acta mathematica scientia,Series A, 2023, 43(6): 1880-1896.

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The Strong Convergence Theorem of Iterative Algorithms for the Fixed Point Problem, a System of Variational Inequalities, and a Split Equilibrium Problem in Hilbert Spaces

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