Inertial hybrid self-adaptive subgradient extragradient method for fixed point of quasi$-\phi-$nonexpansive multivalued mappings and equilibrium problem

Year 2021, , 507 - 522, 30.12.2021

Murtala Harbau

https://doi.org/10.31197/atnaa.822150

Abstract

In this paper, we propose a new inertial self-adaptive subgradient extragradient algorithm for approximating common solution in the set of pseudomonotone equilibrium problems and the set of fixed point of finite family of quasi$-\phi-$nonexpansive multivalued mappings in real uniformly convex Banach spaces and uniformly smooth Banach spaces. The step size n is chosen self adaptively and
estimates of Lipschizt-type constants are dispensed with. Strong convergence of the iterative scheme is established. Our results generalizes and improves several recent results anouced in the literature.

Keywords

Pseudomonotone Equilibrium problem, Inertial self adaptive hybrid method, Multivalued quasi$-\phi-$nonexpansive mapping, Banach spaces

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