Fixed Point Theory, 21(2020), No. 2, 441-452 DOI: 10.24193/fpt-ro.2020.2.31 http://www.math.ubbcluj.ro/ ∼ nodeacj/sfptcj.html A STRONG CONVERGENCE THEOREM FOR AN INERTIAL ALGORITHM FOR A COUNTABLE FAMILY OF GENERALIZED NONEXPANSIVE MAPS C.E. CHIDUME * AND M.O. NNAKWE ** * African University of Science and Technology, Abuja, Nigeria E-mail: cchidume@aust.edu.ng ** African University of Science and Technology, Abuja, Nigeria E-mail: mondaynnakwe@gmail.com Abstract. Let E be a uniformly smooth and strictly convex real Banach space with dual space, E * . In this paper, we present a Krasnoselkii-type inertial algorithm and prove a strong convergence theorem for approximating a common fixed point for a countable family of generalized nonexpansive maps. Furthermore, we apply our theorem and prove a strong convergence theorem for approximating a common fixed point for a countable family of generalized-J -nonexpansive maps. Our theorem is an improvement of the results of Klin-earn et al. (Taiwanese J. of Maths. Vol. 16, No. 6, pp. 1971-1989, Dec. 2012), Chidume et al. (Advances in Fixed Point Theory, Vol. 7, No. 3 (2017), 413-431) and Dong et al. (Optimization Letters, 2017, DOI: 10.1007/s11590-016-1102-9). Finally, we give a numerical experiment to illustrate the efficiency and advantage of the inertial algorithm over an algorithm without inertial term. Key Words and Phrases: Generalized nonexpansive maps, NST -condition, inertial term, fixed point. 2010 Mathematics Subject Classification: 47H09, 47H10, 47J25, 47J05. Research supported from ACBF Research Grant Funds to AUST. References [1] Y. Alber, Metric and generalized projection operators in Banach spaces: properties and ap- plications , Theory and Applications of Nonlinear Operators of Accretive and Monotone Type (A.G. Kartsatos, Ed.), Marcel Dekker, New York, 1996, 15-50. [2] Y. Alber, I. Ryazantseva, Nonlinear Ill Posed problems of Monotone Type , Springer, London, UK, 2006. [3] R.I. Bot, E.R. Csetnek, A hybrid proximal-extragradient algorithm with inertial effects , Numer. Funct. Anal. Optim., 36(2015), 951-963. [4] S.S. Chang, H.W. Joseph Lee, C.K. Chan, W.B. Zhang, A modified halpern-type iteration algorithm for totally quasi-φ-asymptotically nonexpansive mappings with applications , Applied Mathematics and Computation, 218(2012), 6489-6497. [5] C.E. Chidume, K.O. Idu, Approximation of zeros of bounded maximal monotone maps, solutions of Hammerstein integral equations and convex minimization problemss , Fixed Point Theory and Applications, 97(2016), DOI: 10.1186/s13663-016-0582-8. 441