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

## 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## 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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*Tamkang Journal of Mathematics*,

*53*(1), 23-36. https://doi.org/10.5556/j.tkjm.53.2022.3307

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