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Volume 20 (2024)
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JP Journal of Fixed Point Theory and Applications
JP Journal of Fixed Point Theory and Applications
Volume 4, Issue 3, Pages 161 - 181 (December 2009)
A GENERAL ITERATIVE FOR EQUILIBRIUM PROBLEMS OF NONEXPANSIVE SEMIGROUP IN HILBERT SPACES
Yaowaluck Khongtham (Thailand)
Abstract:
In this paper, we introduce a general iterative scheme to find a common element of the set of an equilibrium problem and the set of fixed points of a nonexpansive semigroup in Hilbert spaces. Then we prove a strong convergence theorem for a nonexpansive semigroup mapping to solve a unique solution of the variational inequality which is the optimality condition for the minimization problem. This result extended and improved the corresponding results of Shimizu and Takahashi [10], Wangkeeree [13] and many others.
Keywords and phrases:
fixed point, equilibrium problem, variational inequality, viscosity approximation, nonexpansive semigroup, minimization problem.
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