Extragradient-Proximal Methods for Split Equilibrium and Fixed Point Problems in Hilbert Spaces

• Published in: Vietnam journal of mathematics Vol. 45; no. 4; pp. 651 - 668
• Main Authors: Van Dinh, Bui, Son, Dang Xuan, Anh, Tran Viet
• Format: Journal Article
• Language: English
• Published: Singapore Springer Singapore 01-12-2017; Springer Nature B.V
• Subjects: Algorithms; Cutting parameters; Equilibrium; Equilibrium methods; Mathematics; Mathematics and Statistics; 65K15; Split equilibrium problem; 90C99; Split fixed point problem; Weak and strong convergence; 47H09; Pseudomonotonicity; 65K10; 47J25; Nonexpansive mapping
• ISSN: 2305-221X; 2305-2228
• DOI: 10.1007/s10013-016-0237-4

In this paper, we propose two new extragradient-proximal algorithms for solving split equilibrium and fixed point problems (SEFPP) in real Hilbert spaces, in which the first equilibrium bifunction is pseudomonotone, the second one is monotone, and the fixed point mappings are nonexpansive. By using the extragradient method incorporated with the proximal point algorithm and cutting techniques, we obtain algorithms for solving (SEFPP). Under certain conditions on parameters, the iteration sequences generated by the proposed algorithms are proved to be weakly and strongly convergent to a solution of (SEFPP). Our results improve and extend the previous results given in the literature.