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An iterative technique for solving split equality monotone variational inclusion and fixed point problems

Mewomo Oluwatosin Temitope, Ogbuisi Ferdinard Udochukwu

Journal of Applied Analysis

2023

Vol. 29, nr 1

187--204

The purpose of this paper is to introduce an iterative algorithm for approximating the solution of the split equality monotone variational inclusion problem (SEMVIP) for monotone operators, which is also a solution of the split equality fixed point problem (SEFPP) for strictly pseudocontractive maps in real Hilbert spaces.We establish the strong convergence of the sequence generated by our iterative algorithm. Our result complements and extends some related results in literature.

A strong convergence theorem for a zero of the sum of a finite family of maximally monotone mappings

Wega Getahun B., Zegeye Habtu, Boikanyo Oganeditse A.

Demonstratio Mathematica

2020

Vol. 53, nr 1

152--166

The purpose of this article is to study the method of approximation for zeros of the sum of a finite family of maximally monotone mappings and prove strong convergence of the proposed approximation method under suitable conditions. The method of proof is of independent interest. In addition, we give some applications to the minimization problems and provide a numerical example which supports our main result. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.