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- Title
Contraction-Mapping Algorithm for the Equilibrium Problem over the Fixed Point Set of a Nonexpansive Semigroup.
- Authors
Trinh Ngoc Hai; Le Quang Thuy
- Abstract
In this paper, we consider the proximal mapping of a bifunction. Under the Lipschitz-type and the strong monotonicity conditions, we prove that the proximal mapping is contractive. Based on this result, we construct an iterative process for solving the equilibrium problem over the fixed point sets of a nonexpansive semigroup and prove a weak convergence theorem for this algorithm. Also, some preliminary numerical experiments and comparisons are presented.
- Subjects
FIXED point theory; SEMIGROUP rings; NONEXPANSIVE mappings; LIPSCHITZ spaces; MONOTONIC functions
- Publication
Mathematical Modelling & Analysis, 2019, Vol 24, Issue 1, p43
- ISSN
1392-6292
- Publication type
Article