A strong convergence theorem for solving pseudo-monotone variational inequalities and fixed point problems using subgradient extragradient method in Banach spaces

AIMS Mathematics

Fei Ma¹  Jun Yang¹  Min Yin¹ 

[1] School of Mathematics and Statistics, Xianyang Normal University, Xianyang 712000, Shaanxi, China;

关键词: variational inequalities;    subgradient extragradient method;    fixed point problem;    banach space;    strong convergence;   

DOI  :  10.3934/math.2022279

来源: DOAJ

【 摘 要 】

In this paper, we introduce an algorithm for solving variational inequalities problem with Lipschitz continuous and pseudomonotone mapping in Banach space. We modify the subgradient extragradient method with a new and simple iterative step size, and the strong convergence to a common solution of the variational inequalities and fixed point problems is established without the knowledge of the Lipschitz constant. Finally, a numerical experiment is given in support of our results.

【 授权许可】

Unknown