New algorithms for solving pseudo-monotone variational inequalities in Banach spaces

Year 2024, Early Access, 1 - 20

G. Reza Zamani Eskandanı M. Raeisi R. Lotfikar

https://doi.org/10.15672/hujms.1228124

Abstract

In this paper, we introduce new algorithms for finding a solution of a variational
inequality problem involving pseudo-monotone operator which is also a fixed point
of a Bregman relatively nonexpansive mapping in p-uniformly convex and uniformly
smooth Banach spaces that are more general than Hilbert spaces. We prove weak
and strong convergence theorems for proposed algorithms. Finally, we give some
numerical experiments for supporting our main results.

Keywords

Variational inequality, Pseudo-monotone operator, Bregman distance, Bregman projection

References

• [1] Y. I. Alber, Metric and generalized projection operators in Banach spaces: Properties and applications, in: Theory and Applications of Nonlinear Operators of Accretive and Monotone Type Vol 178 of Lecture Notes in Pure and Applied Mathematics, New York: Dekker, 15-50, 1996.