A modified hybrid projection method for solving generalized mixed equilibrium problems and fixed point problems in Banach spaces

In this paper, we introduce a modified new hybrid projection method for finding the set of solutions of the generalized mixed equilibrium problems and the convex feasibility problems for an infinite family of closed and uniformly quasi‐ $\phi$ ‐asymptotically nonexpansive mappings. Strong convergence theorems are established in a uniformly smooth and strictly convex Banach space which also enjoys the Kadec–Klee property. Our results improve and extend the corresponding results announced by Qin et al. (2010) and many authors.