Open AccessAn efficient iterative method for solving split variational inclusion problem with applications
Author(s) -
Jamilu Abubakar,
Poom Kumam,
Abor Isa Garba,
Muhammad Sirajo Abdullahi,
Abdulkarim Hassan Ibrahim,
Wachirapong Jirakitpuwapat
Publication year - 2022
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2021160
Subject(s) - iterated function , iterative method , variational inequality , convergence (economics) , mathematics , mathematical optimization , preconditioner , extrapolation , scheme (mathematics) , monotone polygon , bounded function , operator (biology) , regular polygon , computer science , mathematical analysis , biochemistry , chemistry , geometry , repressor , transcription factor , economics , gene , economic growth
A new strong convergence iterative method for solving a split variational inclusion problem involving a bounded linear operator and two maximally monotone mappings is proposed in this article. The study considers an iterative scheme comprised of inertial extrapolation step together with the Mann-type step. A strong convergence theorem of the iterates generated by the proposed iterative scheme is given under suitable conditions. In addition, methods for solving variational inequality problems and split convex feasibility problems are derived from the proposed method. Applications of solving Nash-equilibrium problems and image restoration problems are solved using the derived methods to demonstrate the implementation of the proposed methods. Numerical comparisons with some existing iterative methods are also presented.