- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 5 Issue: 4
- Inertial hybrid self-adaptive subgradient extragradient method for fixed point of quasi$-\phi-$nonex...
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
View : 7 | Download : 2
Publication Date : 2021-12-30
Article Type : Research
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