The Ishikawa Subgradient Extragradient Method for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

2020 ◽  
Vol 41 (9) ◽  
pp. 1065-1088
Author(s):  
Manh Hy Duc ◽  
Ha Nguyen Thi Thanh ◽  
Thanh Tran Thi Huyen ◽  
Bui Van Dinh
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Extragradient Method ◽  
Fixed Point Problems ◽  
Subgradient Extragradient Method

scholarly journals Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2680
Author(s):  
Yanlai Song
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Line Search ◽  
Equilibrium Problems ◽  
Recent Literature ◽  
Extragradient Method ◽  
Fixed Point Problems ◽  
Strong Convergence Theorem ◽  
Search Technique ◽  
Line Search Technique

In this paper, we introduce a new hybrid inertial accelerated algorithm with a line search technique for solving fixed point problems for demimetric mapping and split equilibrium problems in Hilbert spaces. The algorithm is inspired by Tseng’s extragradient method and the viscosity method. Then, we establish and prove the strong convergence theorem under proper conditions. Furthermore, we also give a numerical example to support the main results. The main results are new and the proofs are relatively simple and different from those in early and recent literature.

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