A self-adaptive Tseng extragradient method for solving monotone variational inequality and fixed point problems in Banach spaces

Demonstratio Mathematica

Jolaoso Lateef Olakunle¹ 

[1] Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94 Medunsa 0204, Pretoria, South Africa;

关键词: variational inequality;    monotone operator;    self-adaptive;    projection method;    banach spaces;    65k15;    47j25;    65j15;    90c33;   

DOI  :  10.1515/dema-2021-0016

来源: DOAJ

【 摘 要 】

In this paper, we introduce a self-adaptive projection method for finding a common element in the solution set of variational inequalities (VIs) and fixed point set for relatively nonexpansive mappings in 2-uniformly convex and uniformly smooth real Banach spaces. We prove a strong convergence result for the sequence generated by our algorithm without imposing a Lipschitz condition on the cost operator of the VIs. We also provide some numerical examples to illustrate the performance of the proposed algorithm by comparing with related methods in the literature. This result extends and improves some recent results in the literature in this direction.

【 授权许可】

Unknown