Abstract
AbstractIn this paper, we consider split equality generalized mixed equilibrium problem, which is more general than many problems such as split feasibility problem, split equality problem, split equilibrium problem, and so on. We propose a new modified algorithm to obtain strong and weak convergence theorems for split equality generalized mixed equilibrium problem for nonexpansive mappings in Hilbert spaces. Also, we give some applications to other problems. Our results extend some results in the literature.
Highlights
1 Introduction Let H be a real Hilbert space with inner product ·, · and norm ·, C be a nonempty closed convex subset of H, and F : C × C → R be a bifunction, where R is the set of all real numbers
In this paper, inspired by algorithm ( . ), we introduce a modified algorithm to obtain weak and strong convergence results for the split equality generalized mixed equilibrium problem
To solve a generalized mixed equilibrium problem for a bifunction F : C × C → R and mappings T : C → C and φ : C → R, let us assume that the following conditions are satisfied: A
Summary
Let H be a real Hilbert space with inner product ·, · and norm · , C be a nonempty closed convex subset of H, and F : C × C → R be a bifunction, where R is the set of all real numbers. ) converges weakly and strongly to the solution of the split equality generalized mixed equilibrium problem ), we introduce a modified algorithm to obtain weak and strong convergence results for the split equality generalized mixed equilibrium problem.
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