The Split Various Variational Inequalities Problems for Three Hilbert Spaces

Chinda Chaichuay,Atid Kangtunyakarn

doi:10.3390/axioms9030103

Chinda Chaichuay, Atid Kangtunyakarn

Open Access

https://doi.org/10.3390/axioms9030103

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Abstract

There are many methods for finding a common solution of a system of variational inequalities, a split equilibrium problem, and a hierarchical fixed-point problem in the setting of real Hilbert spaces. They proved the strong convergence theorem. Many split feasibility problems are generated in real Hillbert spaces. The open problem is proving a strong convergence theorem of three Hilbert spaces with different methods from the lasted method. In this research, a new split variational inequality in three Hilbert spaces is proposed. Important tools which are used to solve classical problems will be developed. The convergence theorem for finding a common element of the set of solution of such problems and the sets of fixed-points of discontinuous mappings has been proved.

Highlights

We use the following symbols throughout this paper: let H be a real Hilbert space and C be a nonempty closed convex subset of H
The convergence theorem for finding a common element of the set of solution of such problems and the sets of fixed-points of discontinuous mappings has been proved
In [12], Bnouhachem modified a projection process for finding a common solution of a system of variational inequalities, a split equilibrium problem and a hierarchical fixed-point problem in the setting of real Hilbert spaces and proved the strong convergence theorem of the sequence { xn } generated by

Summary

Introduction

We use the following symbols throughout this paper: let H be a real Hilbert space and C be a nonempty closed convex subset of H. In [12], Bnouhachem modified a projection process for finding a common solution of a system of variational inequalities, a split equilibrium problem and a hierarchical fixed-point problem in the setting of real Hilbert spaces and proved the strong convergence theorem of the sequence { xn } generated by. Moudafi [15] introduced the following new split feasibility problem, which is called general split equality problem: Let H1 , H2 , H3 be real Hilbert spaces, C ⊂ H1 , Q ⊂ H2 be two nonempty closed convex sets and. To answer question A, we have created a new tool to prove a strong convergence theorem for three Hilbert spaces to be used for finding the solution of the problem (7) and the fixed points problem of nonspreading and pseudo-nonspreading mappings.

The Split Various Variational Inequality Theorem

Application

Conclusions