The purpose of this paper is to present new hybrid Ishikawa iteration process by the generalized f‐projection operator for finding a common element of the fixed point set for two countable families of weak relatively nonexpansive mappings and the set of solutions of the system of generalized Ky Fan inequalities in a uniformly convex and uniformly smooth Banach space. Furthermore, we show that our new iterative scheme converges strongly to a common element of the afore mentioned sets. As applications, we apply our results to obtain some new results for finding a solution of a common fixed point of two countable in finite families, a system of generalized Ky Fan inequalities and a common zero‐point problem for general B‐monotone and maximal monotone operators in Banach spaces. The results presented in this paper improve and extend important recent results.
