Novel Hybrid Methods for Pseudomonotone Equilibrium Problems and Common Fixed Point Problems

ABSTRACT

The purpose of this article is to introduce some hybrid algorithms for finding a common element of the solution sets of pseudomonotone equilibrium problems and the fixed point sets of nonexpansive mappings in real Hilbert spaces. Our algorithms combine Mann’s iterative methods and Armijo line-search with parallel splitting-up and hybrid techniques. The strong convergence of the proposed algorithms are established without the assumption on the Lipschitz-type condition for the bifunctions involved.

KEYWORDS:

• Armijo linesearch
• equilibrium problem
• fixed point problem
• hybrid method
• parallel splitting-up technique
• pseudomonotonicity

MATHEMATICS SUBJECT CLASSIFICATION:

• 47H09
• 47H10
• 47J25
• 65K10
• 65Y05
• 90C25
• 90C33

Acknowledgments

The authors sincerely thank the editor and anonymous reviewers for their constructive comments, which helped to improve the quality and presentation of this article. The research of first three authors was partially supported by the Vietnam Institute for Advanced Study in Mathematics.