General iterative methods for generalized equilibrium problems and fixed point problems of k-strict pseudo-contractions

Abstract

In this paper, we modify the general iterative method to approximate a common element of the set of solutions of generalized equilibrium problems and the set of common fixed points of a finite family of k-strictly pseudo-contractive nonself mappings. Strong convergence theorems are established under some suitable conditions in a real Hilbert space, which also solves some variation inequality problems. Results presented in this paper may be viewed as a refinement and important generalizations of the previously known results announced by many other authors. MSC: 47H05; 47H09; 47H10

A hybrid viscosity iterative method with averaged mappings for split equilibrium problems and fixed point problems

“…The results presented in this paper generalize and modify the work of Plubtieng and Punpaeng [15], Liu [10], and many others (see [7,17,18], and references therein). We give some numerical examples to show that our iterative scheme is more efficient and promising than the existing one in the literature.…”

“…Considering A = 0 in Theorem 3.1 of Wen and Chen [18], we compare our result with them. Let us consider the sequence {η n i } = { 1 3 } for i = 1, 2, 3.…”

“…implemented by comparing the performance and convergence of Corollaries 1 and 2 with the work of Plubtieng and Punpaeng [15], Liu [10] and Wen and Chen [18]. All the codes were written in Matlab (R2012a).…”

“…In this example, we compare Corollary 2 with Theorem 3.1 of Wen an Chen [18]. Let H 1 = R, C = [0, 100].…”

“…Wen and Chen [18] introduced the general iterative method to approximate a common element of the set of solutions of a generalized equilibrium problem and the set of common fixed points of a finite family of k-strictly pseudo-contractive mappings. They introduced the following iterative scheme: x 1 ∈ H and F 1 (u n , y) + Ax n , y − u n + 1 r n y − u n , u n − x n ≥ 0, ∀y ∈ C, y n = β n u n + (1 − β n ) N i=1 η n i T i u n ,…”