In this paper, we introduce a two-step iterative algorithm to prove a strong convergence result for approximating common fixed points of three contractive-like operators. Our algorithm basically generalizes an existing algorithm..Our iterative algorithm also contains two famous iterative algorithms: Mann iterative algorithm and Ishikawa iterative algorithm. Thus our result generalizes the corresponding results proved for the above three iterative algorithms to a class of more general operators. At the end, we remark that nothing prevents us to extend our result to the case of the iterative algorithm with error terms.<\/p>\r\n","references":"[1]\tV. Berinde, A convergence theorem for some mean value fixed point iterations procedures, Dem. Math., 38(1)2005, 177-184.\r\n[2]\tS.K. Chatterjea, Fixed point theorems, C.R. Acad. Bulgare Sci., 25 (1972), 727-730.\r\n[3]\tH. Fukhar-ud-din and S. H. Khan, Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications, J. Math. Anal. Appl. 328 (2007), 821-829.\r\n[4]\tC.O. Imoru, M.O. Olatinwo, On the stability of Picard and Mann iteration processes, Carpathian Journal of Mathematics, 19, 155-160 (2003).\r\n[5]\tS. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44 (1974), 147-150.\r\n[6]\tL. S. Liu, Ishikawa and Mann Iteration process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194(1) (1995), 114-125.\r\n[7]\t R. Kannan, Some results on fixed points,Bull. Calcutta Math. Soc., 10(1968), 71-76.\r\n[8]\tS.H. Khan, A Picard-Mann hybrid iterative process, Fixed Point Theory and Applications 2013, 2013:69.\r\n[9]\tS.H. Khan, Approximating Common fixed points by an iterative process involving two steps and three mappings, Journal of Concrete and Applicable Mathematics, Vol 8, number 3, 407-415, 2010.\r\n[10]\tS.H. Khan, Fixed points of quasi-contractive type operators in normed spaces by a three-step iteration process, Proceedings of the World Congress on Engineering 2011 Vol I, WCE 2011, July 6 - 8, 2011, London, U.K, pp 144-147.\r\n[11]\tSafeer Hussain Khan, Hafiz Fukhar-ud-din, Common fixed points of two finite families of quasi-contractive type operators in normed spaces, 2nd Annual International Conference on Computational Mathematics, Computational Geometry & Statistics (CMCGS 2013), Organized by Global Science & Technology Forum (GSTF), held in Singapore 4-5 February, 2013.\r\n[12]\tW.R. Mann, Mean value methods in iterations, Proc. Amer. Math. Soc., 4 (1953), 506-510.\r\n[13]\tY. Xu, Ishikawa and Mann Iteration process with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998), 91-101.\r\n[14]\tY. Yao, Y.Chen,Weak and strong convergence of a modified Manniteration for asymptotically nonexpansive mappings, Nonlin. Funct. Anal. Appl., 12(2007), 307-315.\r\n[15]\t T. Zamfirescu, Fix point theorems in metric spaces, Arch. Math. (Basel), 23(1972), 292-298.\r\n","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 90, 2014"}