Weak Convergence Theorems for Generalized Mixed Equilibrium Problems, Monotone Mappings and Pseudocontractive Mappings

Abstract

Abstract. In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a generalized mixed equilibrium problem related to a continuous monotone mapping, the set of solutions of a variational inequality problem for a continuous monotone mapping, and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces. Weak convergence for the proposed iterative algorithm is proved. Our results improve and extend some recent results in the literature.

Weak and strong convergence theorems for nonlinear mappings and system of generalized mixed equilibrium problems in Hilbert spaces

“…And notice that Ω(x, y) = Θ(x, y) + Bx, y − x + ϕ(y) − ϕ(x) satisfies conditions (A1)-(A4) (see [10]). Additionally, if B ≡ 0 and ϕ ≡ 0, GMEP(Θ, ϕ, B) reduces to EP(Θ), that is,…”

Modified hybrid iterative methods for generalized mixed equilibrium, variational inequality and fixed point problems

“…In 2015 Jung [17] also proposed an iterative method for GMEP (1.1) related to a continuous monotone mapping B, the VIP (1.5) for a continuous monotone mapping F and a continuous pseudocontractive mapping T and proved weak convergence to a point w ∈ GMEP(Θ, ϕ, B) ∩ VI(C, F) ∩ Fix(T ).…”