Abstract
The main purpose of this paper is by using a hybrid algorithm to find a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for variational inequality problems, and the set of common fixed points for a infinite family of total quasi‐ϕ‐asymptotically nonexpansive multivalued mapping in a real uniformly smooth and strictly convex Banach space with Kadec‐Klee property. The results presented in this paper improve and extend some recent results announced by some authors.
Highlights
Θ u, y ψ y − ψ u ≥ 0, ∀y ∈ C, 1.4 which is called the mixed equilibrium problem MEP 1 . ii If Θ ≡ 0, the problem 1.2 is equivalent to finding u ∈ C such that
In 2009, Zhang 10 proved the strong convergence theorem for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions for variational inequality problems, and the set of fixed points of a finite family of quasiφ-asymptotically nonexpansive mappings in a uniformly smooth and uniformly convex Banach space
Motivated and inspired by the researches going on in this direction, the purpose of this paper is by using the hybrid iterative algorithm to find a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions for variational inequality problems, and the set of fixed points of a infinite family of total quasiφ-asymptotically nonexpansive multivalued mappings in a uniformly smooth and strictly convex Banach space with Kadec-Klee property
Summary
Throughout this paper, we always assume that X is a real Banach space with the dual X∗, C is a nonempty closed convex subset of X, and J : X → 2X is the normalized duality mapping defined by. In 2009, Zhang 10 proved the strong convergence theorem for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions for variational inequality problems, and the set of fixed points of a finite family of quasiφ-asymptotically nonexpansive mappings in a uniformly smooth and uniformly convex Banach space. Motivated and inspired by the researches going on in this direction, the purpose of this paper is by using the hybrid iterative algorithm to find a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions for variational inequality problems, and the set of fixed points of a infinite family of total quasiφ-asymptotically nonexpansive multivalued mappings in a uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in the paper improve and extend some recent results announced by some authors
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