Open AccessA Method for Solving the Variational Inequality Problem and Fixed Point Problems in Banach Spaces
Author(s) -
Wongvisarut Khuangsatung,
Atid Kangtunyakarn
Publication year - 2021
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.53.2022.3307
Subject(s) - mathematics , banach space , variational inequality , fixed point , convergence (economics) , fixed point theorem , eberlein–šmulian theorem , pure mathematics , set (abstract data type) , discrete mathematics , mathematical analysis , lp space , computer science , economics , programming language , economic growth
The purpose of this research is to modify Halpern iteration’s process for finding a common element of the set of solutions of a variational inequality problem and the set of fixed points of a strictly pseudo contractive mapping in q-uniformly smooth Banach space. We also introduce a new technique to prove a strong convergence theorem for a finite family of strictly pseudo contractive mappings in q-uniformly smooth Banach space. Moreover, we give a numerical result to illustrate the main theorem.