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On Picard iterations for strongly accretive and strongly pseudo-contractive Lipschitz mappings. (English) Zbl 1225.47092
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.

##### MSC:
 47J25 Iterative procedures involving nonlinear operators 47H06 Nonlinear accretive operators, dissipative operators, etc. 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47J05 Equations involving nonlinear operators (general) 65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
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