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Novel Hybrid Methods for Pseudomonotone Equilibrium Problems and Common Fixed Point Problems |
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| Authors: | L. Q. Thuy P. K. Anh L. D. Muu T. N. Hai |
| Affiliation: | 1. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnamthuy.lequang@hust.edu.vn;3. Department of Mathematics, Vietnam National University, Hanoi, Vietnam;4. TIMAS, Thang Long University, Hanoi, Vietnam;5. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam |
| 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 |