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Generalized split null point of sum of monotone operators in Hilbert spaces

Mebawondu Akindele A., Abass Hammed A., Oyewole Olawale K., Aremu Kazeem O., Narain Ojen K.

Demonstratio Mathematica

2021

Vol. 54, nr 1

359--376

In this paper, we introduce a new type of a generalized split monotone variational inclusion (GSMVI) problem in the framework of real Hilbert spaces. By incorporating an inertial extrapolation method and an Halpern iterative technique, we establish a strong convergence result for approximating a solution of GSMVI and fixed point problems of certain nonlinear mappings in the framework of real Hilbert spaces. Many existing results are derived as corollaries to our main result. Furthermore, we present a numerical example to support our main result and propose an open problem for interested researchers in this area. The result obtained in this paper improves and generalizes many existing results in the 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.