A new hybrid cyclic algorithm for two finite families of strictly asymptotically pseudocontractive mappings

The purpose of this paper is to propose a new hybrid cyclic algorithm for two finite families of strictly asymptotically pseudocontractive mappings and to establish a strong convergence theorem to approximate common fixed point. The main result of the paper is an improvement and generalization of the well known corresponding results. It also provides an affirmative answer to an interesting problem raised by Marino and Xu [Weak and strong convergence theorem for κ-strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007), 336-349]. 2010 Mathematics Subject Classification. 47H09, 47H10