  We consider a class of generalized nonexpansive mappings introduced by
Karapinar [5] and seen as a generalization of Suzuki (C)-condition. We prove
some weak and strong convergence theorems for approximating fixed points of
such mappings under suitable conditions in uniformly convex Banach spaces. Our
results generalize those of Khan and Suzuki [4] to the case of this kind of
mappings and, in turn, are related to a famous convergence theorem of Reich [2]
on nonexpansive mappings.
