Open AccessA new algorithm for split variational inclusion and fixed point problems in Banach spaces
Author(s) -
Puangpee Jenwit,
Suantai Suthep
Publication year - 2020
Publication title -
computational and mathematical methods
Language(s) - English
Resource type - Journals
ISSN - 2577-7408
DOI - 10.1002/cmm4.1078
Subject(s) - banach space , mathematics , fixed point , inclusion (mineral) , point (geometry) , algorithm , pure mathematics , mathematical analysis , geometry , physics , thermodynamics
In this article, we introduce a new algorithm for finding a solution element of the split variational inclusion problem which is also a fixed point of a nonexpansive mapping in a uniformly convex and smooth Banach space. A strong convergence theorem of the proposed algorithm is established under some suitable control conditions. Our main result can reduce to study several variational inclusion problems, null point problems, and fixed point problems in both Hilbert and Banach spaces. Numerical experiments to illustrate the convergence behavior of our proposed algorithm are given. Moreover, we also apply our results to solve the image restoration problems.