Convergence theorems for split equality mixed equilibrium problems with applications

Zhaoli Ma,Lin Wang,Shih-Sen Chang,Wen Duan

doi:10.1186/s13663-015-0281-x

Abstract

AbstractIn this paper, we introduce a new algorithm for solving split equality mixed equilibrium problems in the framework of infinite-dimensional real Hilbert spaces. The strong and weak convergence theorems are obtained. As application, we shall utilize our results to study the split equality mixed variational inequality problem and the split equality convex minimization problem. Our results presented in this paper improve and extend some recent corresponding results.

Highlights

Let H be a real Hilbert space with the inner product ·, · and the norm ·
In this paper, motivated by the above works and related literature, we introduce a new algorithm for solving split equality mixed equilibrium problems in the framework of infinite-dimensional real Hilbert spaces
In Theorem . taking B = I and H = H, from Theorem . we can obtain the following convergence theorem for general split equilibrium problem ( . )

Summary

Introduction

Let H be a real Hilbert space with the inner product ·, · and the norm ·. Let F : C ×C → R and G : Q×Q → R be nonlinear bifunctions, let φ : C → R ∪ {+∞} and φ : Q → R ∪ {+∞} be proper lower semi-continuous and convex functions such that C ∩ dom φ = ∅ and Q ∩ dom φ = ∅, and let A : H → H and B : H → H be two bounded linear operators, the split equality mixed equilibrium problem (SEMEP) is to find x∗ ∈ C and y∗ ∈ Q such that

Results

Conclusion