en تخصصي Special پژوهشي Research paper <p>We construct one-step iterative process for an &alpha;- nonexpansive mapping and a mapping satisfying condition (C) in the framework of a convex metric space. We study -convergence and strong convergence of the iterative process to the common fixed point of the mappings. Our results are new and are valid in hyperbolic spaces, CAT(0) spaces, Banach spaces and Hilbert spaces, simultaneously.</p> Convex metric space, α-Nonexpansive mapping, Condition(C), Common fixed point, One-step iterative process, Convergence. 167 179 http://ijmsi.ir/browse.php?a_code=A-10-2278-1&slc_lang=en&sid=1 H. Fukhar-ud-din 10031947532846007054 10031947532846007054 Yes Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals