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Ćirić, Ljubomir; Rafiq, Arif; Cakić, Nenad

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

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 12, 4332-4337 (2009).
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.

Cited in 2 Reviews
Cited in 3 Documents

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

Keywords:

Banach space; Lipschitzian mapping; strictly pseudo-contractive mapping; Picard iteration; asymptotically pseudo-contractive mappings; Banach spaces

Citations:

Zbl 1057.47003; Zbl 0870.47039
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Full Text: DOI

References:

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