In this paper, we first prove strong convergence theorems for the modified Ishikawa iteration process of quasi-nonexpansive (nonexpansive) nonself-mappings satisfying Condition A. Next, we prove strong convergence theorems for the modified Ishikawa iteration process of quasi-nonexpansive (nonexpansive) nonself-mappings when  is contained in a compact subset of a real uniformly convex Banach space. Our results generalize the theorems due to Shahzad [1] and Tan-Xu [2].

strong convergence, Condition A, fixed point, nonexpansive mapping.