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Modified hybrid block iterative algorithm for convex feasibility problems and generalized equilibrium problems for uniformly quasi-\(\varphi \)-asymptotically nonexpansive mappings. (English) Zbl 1206.47084

Summary: We introduce a modified block hybrid projection algorithm for solving convex feasibility problems for an infinite family of closed and uniformly quasi-\(\varphi \)-asymptotically nonexpansive mappings and the set of solutions of the generalized equilibrium problems. We obtain a strong convergence theorem for the sequences generated by this process in a uniformly smooth and strictly convex Banach space with the Kadec-Klee property. The results presented in this paper improve and extend some recent results.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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