An explicit iterative algorithm for k-strictly pseudo-contractive mappings in Banach spaces

Let E be a real uniformly smooth Banach space. Let K be a nonempty bounded closed and convex subset of E. Let T : K -> K be a strictly pseudo-contractive map and f be a contraction on K. Assume F(T):= {x is an element of K :Tx - x} not equal empty set. Consider the following iterative algorithm in K given by x(n+1) = alpha(n)f(x(n)) + beta(n)x(n) + gamma(n)S(n)x(n), where S-n : K -> K is a mapping defined by S(n)x := (1 - delta(n))x + delta(n)Tx. It is proved that the sequence {x(n)} generated by the above iterative algorithm converges strongly to a fixed point of T. Our results mainly extend and improve the results of [C. O. Chidume, G. De Souza, Nonlinear Anal., 69 (2008), 2286-2292] and [J. Balooee, Y. J. Cho, M. Roohi, Numer. Funct. Anal. Optim., 37 (2016), 284-303]. (C) 2016 All rights reserved.