Two algorithms for solving mixed equilibrium problems and fixed point problems in Hilbert spaces

• Published in: Annali dell'Università di Ferrara. Sezione 7. Scienze matematiche Vol. 67; no. 2; pp. 253 - 268
• Main Author: Farid, Mohammad
• Format: Journal Article
• Language: English
• Published: Milan Springer Milan 01.11.2021; Springer Nature B.V
• Subjects: Algebraic Geometry; Analysis; Fixed points (mathematics); Geometry; Hilbert space; History of Mathematical Sciences; Iterative algorithms; Iterative methods; Mathematics; Mathematics and Statistics; Numerical Analysis; Subgradient extragradient method; Iterative scheme; 47H10; Fixed-point problem; 49J30; 90C99; Generalized skew-symmetric bi-functions; 47H17; System of mixed equilibrium problems; Nonexpansive mapping
• ISSN: 0430-3202; 1827-1510
• DOI: 10.1007/s11565-021-00380-8

Our study in this paper is focused on mixed equilibrium problems as well as combination with and fixed point problems in real Hilbert spaces. We introduce a new extension of a skew-symmetric bi-functions, called generalized skew-symmetric bi-functions. Two iterative methods based on the subgradient extragradient method is presented and their weak convergence theorems are proved under some mild assumptions. Further, we discuss some numerical examples to demonstrate the applicability of the iterative algorithm. The methods and analysis is new and extend several related result in the literature.