Summary: We speed up the convergence of the Picard sequence of iterations for strongly accretive and strongly pseudo-contractive mappings. Our results improve the results of C. E. Chidume
[“Picard iterations for strongly accretive and strongly pseudocontractive Lipschitz maps” (ICTP Preprint No. IC2000098) (2000); “Iterative algorithms for non-expansive mappings and some of their generalizations”, in: Ravi P. Agarwal (ed.) et al., Nonlinear analysis and applications: To V. Lakshmikantham on his 80th birthday, Vol. 1 (Dordrecht: Kluwer), 383–429 (2003; Zbl 1057.47003
)], L.-W. Liu
[Proc. Am. Math. Soc. 125, No. 5, 1363–1366 (1997; Zbl 0870.47039
)], and some other known results. The technique of the proof presented in this paper is different from the technique used by Chidume.