An iterative method for total quasi-\(\phi\)-asymptotically nonexpansive semi-groups and generalized mixed equilibrium problems in Banach spaces. (English) Zbl 1410.47030
Summary: In this paper, we introduce an iterative scheme by the modified Halpern- Mann-type for total quasi-\(\phi\)-asymptotically nonexpansive semi-groups and prove the strong convergence theorem using our new iterative process which converges strongly to a common element of the set of common fixed points for total quasi-\(\phi\)-asymptotically nonexpansive semi-groups and the set of solutions of generalized mixed equilibrium problem in a uniformly smooth and strictly convex Banach space with the Kadec-Klee property using the properties of the generalized \(f\)-projection operator. Our results extend and improve the corresponding recent results in the literature.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
Keywords:
total quasi-\(\phi\)-asymptotically nonexpansive semi-group; quasi-\(\phi\)-asymptotically nonexpansive semi-group; quasi-\(\phi\)-nonexpansive semi-group; generalized mixed equilibrium problemReferences:
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