Hybrid method for equilibrium problems and fixed point problems of finite families of nonexpansive semigroups

Split equality problem with equilibrium problem, variational inequality problem, and fixed point problem of nonexpansive semigroups

“…By similar argument we obtain that y ∈ Fix(S). Since lim n→∞ η n − z n = lim n→∞ U Φ κ n,1 z n − z n = 0, and z n x, we have x ∈ EP(Φ), (see [18] for details). Similarly we have y ∈ EP(Ψ).…”

“…In the last years, many authors studied the problems of finding a common element of the set of fixed points of nonlinear operator and the set of solutions of an equilibrium problem (and the set of solutions of variational inequality problem) in the framework of Hilbert spaces, see, for instance, [2,11,18,20,24,31] and the references therein. The motivation for studying such a problem is in its possible application to mathematical models whose constraints can be expressed as fixed-point problems and/or equilibrium problem.…”

A shrinking projection extragradient algorithm for equilibrium problem and fixed point problem

“…For example, see; [7,10,14]. On the other hand, Tada and Takahashi [26] introduced the CQ method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping T in a Hilbert space H. In recent years, the problem to find a common point of the solution set of equilibrium problem and the set of fixed points of a nonexpansive mapping becomes an attractive field for many researchers (see [9,12,21,26,27,28]). We recall the following well-known definitions.…”

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.…”