Novel Hybrid Methods for Pseudomonotone Equilibrium Problems and Common Fixed Point Problems
L. Q. Thuy, Pham Ky Anh, L. D. Muu, Trinh Ngoc Hai · Numerical Functional Analysis and Optimization · 2017
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.