On a Mann type implicit iteration process for strictly pseudocontraction semigroups

Abstract

The purpose of this paper is to study the strong and weak convergence of an implicity iteration process for strictly pseudocontractive semigroups in general Banach spaces. The results presented in this paper extend and improve recent results of some people. Zhang [{\it Acta Mathematica Sinica, English Series,} {\bf 26} 337-344 (2010)], Zhang [{\it Appl. Math. Mech. -Engl. Ed.}, {\bf 30}, 145-152 (2009)], Zhou [{\it Nonlinear Anal.}, {\bf 68}, 2977-2983 (2008)], Chen, et al. [{\it J. Math. Anal.,} {\bf 314}, 701-709 (2006)],  Osilike [{\it J. Math. Appl.,} {\bf 294}, 73-81 (2004)] and Xu and Oir [ {\it Numer. Funct. Anal. Optim.,} {\bf 22}, 767-773 (2001)].