Iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo-contractive mappings in Banach spaces

In this article, we prove some new convergence theorems of the Ishikawa and Mann iteration sequences for strongly accretive and strongly pseudo-contractive mappings by using the new inequality and the new approximation methods. Our main results improve and extend the corresponding results of [J. Math. Anal. Appl. 151 (1990), 453-461; Proc. Amer. Math. Sec. 120 (1994), 545-551; J. Math. Appl. 192 (1995), 502-518; J. Math. Anal. Appl. 174 (1993), 441-449; Acta Appl. Math. 32 (1993), 183-196; Nonlinear Anal. TMA 24 (1995), 981-987; J. Math. Anal. Appl. 178 (1993), 9-21; Proc. Amer. Math. Sec. 125(6) (1997), 1705-1709]. (C) 1998 Academic Press.