Strong convergence theorems for equilibrium problems and fixed point problem of multivalued nonexpansive mappings via hybrid projection method

Abstract

In this paper, a new iterative process by the hybrid projection method is constructed. Strong convergence of the iterative process to a common element of the set of common fixed points of a finite family of generalized nonexpansive multivalued mappings and the solution set of two equilibrium problems in a Hilbert space is proved. Our results extend some important recent results. MSC: 47H10; 47H09

Hybrid projection algorithms for total asymptotically strict quasi-ϕ -pseudo-contractions

“…However, It is known that the Mann iterative algorithm only has weak convergence, even for nonexpansive mappings in infinite-dimensional Hilbert spaces; for more details, see [24,31] and the reference therein. To obtain the strong convergence of the Mann iterative algorithm so-called hybrid projection algorithms have been considered; for more details, see [1,11,12,15,16,17,28,29,40,41,42] and the references therein.…”

Halpern-Type Iterative Algorithm for an Infinite Family of Relatively Quasi-Nonexpansive Multivalued Mappings and Equilibrium Problem in Banach Spaces

“…Theory of nonexpansive multivalued mappings is harder than the corresponding theory of nonexpansive single valued mappings. Different iterative processes have been used to approximate fixed points of multivalued nonexpansive mappings (see [1][2][3][4][5][6][7]).…”

Strong Convergence Results for Equilibrium Problems and Fixed Point Problems for Multivalued Mappings

“…Many researchers have studied various iteration processes for finding a common element of the set of solutions of the equilibrium problems and the set of fixed points of a class of nonlinear mappings. For example, see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”