scholarly journals A self-adaptive inertial subgradient extragradient method for pseudomonotone equilibrium and common fixed point problems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Lateef Olakunle Jolaoso ◽  
Maggie Aphane
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Extragradient Method ◽  
Fixed Point Problems ◽  
Subgradient Extragradient Method ◽  
Self Adaptive

scholarly journals Halpern-Subgradient Extragradient Method for Solving Equilibrium and Common Fixed Point Problems in Reflexive Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 743
Author(s):  
Annel Thembinkosi Bokodisa ◽  
Lateef Olakunle Jolaoso ◽  
Maggie Aphane
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Reflexive Banach Space ◽  
Extragradient Method ◽  
Convergence Result ◽  
Fixed Point Problems ◽  
Subgradient Extragradient Method ◽  
Reflexive Banach Spaces ◽  
Mild Conditions ◽  
Lipschitz Constants

In this paper, using the concept of Bregman distance, we introduce a new Bregman subgradient extragradient method for solving equilibrium and common fixed point problems in a real reflexive Banach space. The algorithm is designed, such that the stepsize is chosen without prior knowledge of the Lipschitz constants. We also prove a strong convergence result for the sequence that is generated by our algorithm under mild conditions. We apply our result to solving variational inequality problems, and finally, we give some numerical examples to illustrate the efficiency and accuracy of the algorithm.

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