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J. Korean Math. Soc. 2015; 52(6): 1179-1194
Printed November 1, 2015
https://doi.org/10.4134/JKMS.2015.52.6.1179
Copyright © The Korean Mathematical Society.
Weak convergence theorems for generalized mixed equilibrium problems, monotone mappings and pseudocontractive mappings
Jong Soo Jung
Dong-A University
In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a generalized mixed equilibrium problem related to a continuous monotone mapping, the set of solutions of a variational inequality problem for a continuous monotone mapping, and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces. Weak convergence for the proposed iterative algorithm is proved. Our results improve and extend some recent results in the literature.
Keywords: generalized mixed equilibrium problem, fixed point, continuous pseudocontractive mapping, continuous monotone mapping, variational inequality, metric projection, weak convergence
MSC numbers: 47H05, 47H09, 47H10, 47J05, 47J20, 47J25
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