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

Authors : Murtala HARBAU

Pages : 507-522

Doi:10.31197/atnaa.822150

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Publication Date : 2021-12-30

Article Type : Research Paper

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