IMPLICIT AND EXPLICIT ITERATIVE PROCESS WITH ERRORS FOR COMMON FIXED POINTS OF A FINITE FAMILY OF STRICTLY PSEUDOCONTRACTIVE MAPPINGS

In this paper, a necessary and sufficient conditions for the strong convergence to a common fixed point of a finite family of strictly pseudocontractive mappings of Browder-Petryshyn type are proved in an arbitrary real Banach spaces using a implicit iteration scheme with errors. The results presented in this paper not only correct some mistakes appeared in the paper by Y. Su and S. Li [Composite implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl., 320(2006), 882-891] but also improve and extend some recent results by M.O. Osilike [M.O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl., 294(2004), 73-81], and F. Gu [The new composite implicit iteration process with errors for common fixed points of a finite of strictly pseudocontractive mappings, J. Math. Anal. Appl., 329(2007), 766-776]. Moreover, in this paper the methods of proof of main results are also different from that of Osilike, Su and Li.