Strong convergence of composite general iterative methods for one-parameter nonexpansive semigroup and equilibrium problems
Xin Xiao, Suhong Li, Lihua Li, Heping Song, Lingmin Zhang · Journal of Inequalities and Applications · 2012
Abstract In this paper, we introduce both explicit and implicit schemes for finding a common element in the common fixed point set of a one-parameter nonexpansive semigroup {T(s)| 0 ≤ s < ∞} and in the solution set of an equilibrium problems which is a solution of a certain optimization problem related to a strongly positive bounded linear operator. Strong convergence theorems are established in the framework of Hilbert spaces. As an application, we consider the optimization problem of a k-strict pseudocontraction mapping. The results presented improve and extend the corresponding results of many others. 2000 AMS Subject Classification: 47H09; 47J05; 47J20; 47J25.