Convergence theorems by extragradient method in Banach spaces

2015/09/07 by Zeynab Jouymandi, Jouymandi, Zeynab, Fridoun Moradlou +1
Computer Science · Mathematics · #Optimization and Variational Analysis #Fixed Point Theorems Analysis #Advanced Optimization Algorithms Research

paper · pdf · doi:10.48550/arxiv.1509.02018

Abstract

In this paper, using generalized metric projection, we propose a new extragradient method for finding a common element of the solutions set of a generalized equilibrium problem and a variational inequality for an α-inverse-strongly monotone operator and fixed points of two relatively nonexpansive mappings in Banach spaces. We prove strong convergence theorems by this method under suitable conditions. A numerical example is given to illustrate the usability of our results.

Citations

• Metric and Generalized Projection Operators in Banach Spaces: Properties\n and Applications

Related

• Strong convergence theorems by a new hybrid method for equilibrium problems and relatively nonexpansive mappings in Banach spaces
• Extragradient and linesearch algorithms for solving equilibrium problems and fixed point problems in Banach spaces
• A New Shrinking projection Algorithm for an infinite family of Bregman weak relatively nonexpansive mappings in a Banach Space
• Convergence theorem for solving generalized mixed equilibrium problem and finding fixed point of a weak Bregman relatively nonexpansive mapping in Banach spaces
• Weak Convergence Theorem by a New Extragradient Method for Fixed Point Problems and Variational Inequality Problems