A Method for Solving the Variational Inequality Problem and Fixed Point Problems in Banach Spaces

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Published: Apr 14, 2021
DOI: https://doi.org/10.5556/j.tkjm.53.2022.3307
Keywords:
Strictly pseudo contractive mapping; Inverse strongly monotone accretive operator; Variational inequality problem; $q$-uniformly smooth Banach space

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Wongvisarut Khuangsatung
Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Pathumthani, 12110, Thailand.
https://orcid.org/0000-0001-8065-5784
Atid Kangtunyakarn
Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang

Abstract




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.




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How to Cite
Khuangsatung, W., & Kangtunyakarn, A. (2021). A Method for Solving the Variational Inequality Problem and Fixed Point Problems in Banach Spaces. Tamkang Journal of Mathematics, 53(1), 23–36. https://doi.org/10.5556/j.tkjm.53.2022.3307
Issue
Vol. 53 No. 1 (2022)
Section
Papers
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