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

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)359-376
Number of pages18
JournalDemonstratio Mathematica
Volume54
Issue number1
DOIs
Publication statusPublished - 1 Jan 2021
Externally publishedYes

Keywords

  • firmly nonexpansive
  • fixed point problem
  • generalized split monotone variational inclusion
  • inertial iterative scheme

Fingerprint

Dive into the research topics of 'Generalized split null point of sum of monotone operators in Hilbert spaces'. Together they form a unique fingerprint.

Cite this