Abstract
Very recently, Ceng and Yao [L. C. Ceng, J. C. Yao, A relaxed extragradient-like method for a generalized mixed equilibrium problem, a general system of generalized equilibria and a fixed point problem, Nonlinear Anal., 72 (2009), 1922-1937, suggested and analyzed a relaxed extragradient-like method for finding a common solution of a generalized mixed equilibrium problem, a general system of generalized equilibria and a fixed point problem of a strict pseudocontractive mapping in a Hilbert space. In this paper, based on the authors' iterative method, we introduce a modification of the relaxed extragradient-like method for finding a common solution of a generalized mixed equilibrium problem with perturbed mapping, a general system of generalized nonlinear mixed composite-type equilibria and a fixed point problem of a strict pseudocontractive mapping in a Hilbert space, and then obtain a strong convergence theorem. Utilizing this theorem, we establish some new strong convergence results in fixed point problems, variational inequalities, mixed equilibrium problems and systems of generalized nonlinear mixed composite-type equilibria in Hilbert spaces.
Citation
Hui-Ying Hu. Lu-Chuan Ceng. "A General System of Generalized Nonlinear Mixed Composite-Type Equilibria in Hilbert Spaces." Taiwanese J. Math. 15 (3) 927 - 959, 2011. https://doi.org/10.11650/twjm/1500406276
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