Explicit Iteration Methods for Solving Variational Inequalities in Banach Spaces

Pham Thanh Hieu; Nguyen Thi Thu Thuy; Jean Jacques Strodiot

doi:10.1007/s40840-017-0494-8

Explicit Iteration Methods for Solving Variational Inequalities in Banach Spaces

Pham Thanh Hieu, Nguyen Thi Thu Thuy, Jean Jacques Strodiot

Research output: Contribution to journal › Article

Abstract

The problem of finding a solution of a variational inequality over the set of common fixed points of a nonexpansive semigroup is considered in a real and uniformly convex Banach space without imposing the sequential weak continuity of the normalized duality mapping. Two new explicit iterative methods are introduced based on the steepest-descent method, and conditions are given to obtain their strong convergence. A numerical example is showed to illustrate the convergence analysis of the proposed methods.

Original language	English
Pages (from-to)	467-483
Number of pages	17
Journal	Bulletin of the Malaysian Mathematical Sciences Society
Volume	42
Issue number	2
DOIs	https://doi.org/10.1007/s40840-017-0494-8
Publication status	Published - 15 Mar 2019

Keywords

Accretive mapping
Common fixed point
Explicit method
Nonexpansive semigroup
Variational inequality

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10.1007/s40840-017-0494-8

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Hieu, P. T., Thuy, N. T. T., & Strodiot, J. J. (2019). Explicit Iteration Methods for Solving Variational Inequalities in Banach Spaces. Bulletin of the Malaysian Mathematical Sciences Society, 42(2), 467-483. https://doi.org/10.1007/s40840-017-0494-8

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