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On Picard iterations for strongly accretive and strongly pseudo-contractive Lipschitz mappings

✍ Scribed by Ljubomir Ćirić; Arif Rafiq; Nenad Cakić

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
372 KB
Volume
70
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this note, 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 Chidume [C.E. Chidume, Picard iteration for strongly accretive and strongly pseudo-contractive Lipschitz maps, ICTP Preprint no. IC2000098; C.E. Chidume, Iterative Algorithms for Non-expansive Mappings and Some of Their Generalizations, in: Nonlinear Analysis and Applications: To V. Lakshmikantham on his 80th Birthday, vol. 1, 2, Kluwer Acad. Publ, Dordrecht, 2003, pp. 383-429], and Liu [L. Liu, Approximation of fixed points of a strictly pseudo-contractive mapping, Proc. Amer. Math. Soc. 125 (2) (1997) 1363-1366], and some other known results. The technique of the proof, presented in this paper, is different from the technique used by Chidume.

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