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 ∈ K : T x = x} =/ ∅. Consider the following iterative algorithm in K given by xn+1 = αnf (xn) + βnxn + γnSnxn, where Sn : K → K is a mapping defined by Snx := (1 − δn)x + δnT x. It is proved that the sequence {xn} 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].