Modified hybrid block iterative algorithm for convex feasibility problems and generalized equilibrium problems for uniformly quasi-\(\varphi \)-asymptotically nonexpansive mappings (Q1957572)

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.