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2004, br. 8-1, str. 25-31
Fixed points of some classes of nonexpansive mappings
(naslov ne postoji na srpskom)
Univerzitet u Kragujevcu, Učiteljski fakultet, Jagodina
Ključne reči: normed ƒλ-orbitally complete spaces with λ-uniformly convex sphere; nonexpansive operator; λ-orbit; fixed point; extremal point; star-shaped sets
Sažetak
(ne postoji na srpskom)
In this paper we proves the convergence of a convex sequence xn = λxn-1 + (1 - λ)ƒ(xn-1), λ Є (0,1), to a fixed point of the nonexpansive completely continuous operator in the normed ƒ λ -orbitally complete spaces with λ-uniformly convex sphere. Further we shall prove some fixed point theorems of the star-shaped sets.
Reference
Browder, F.E. (1965) Nonexpansive nonlinear operators in a Banach space. Proc Natl Acad Sci USA, 54, 1041-1044
Gohde, D. (1965) Zum Prinzip der kontraktiven Abbildung. Mathematische Nachrichten, 30(3-4): 251
Kannan, R. (1968) Some results on fixed points I. Bull. Calcutta Math, Soc, 60, 71-76
Karlovitz, L.A. (1976) Some fixed point results for nonexpansive mappings: Fixed point theory and it's applications. New York-San Diego, itd: Academic Press, 91-103
Kirk, W.A. (1965) A fixed point theorem for mappings which do not increase distances. Amer. Math. Monthly, 72, 1004-1006
Krasnoselskij, M.A. (1955) Two remarks on the method of successive approximations. Uspekhi Matematicheskikh Nauk, 10, 63, 123-127
Mijajlović, B.S. (1999) Fiksne tačke, mere nekompaktnosti i prošireno konveksne funkcije. Niš: Filozofski fakultet, doktorska teza
Reinermann, J. (1974) Fixed point theorems for nonexpansive mappings on starshaped domains. Bonn: Ber. Ges. Math. Daten
Reinermann, J., Schoneberg, R. (1976) Some results in the fixed point theory of nonexpansive mappings and generalized contractions: Fixed point theory and its applications. Academic Press
Tasković, M.R. (1993) Nonlinear functional analysis: Fundamental elements of theory. Beograd: Zavod za udžbenike i nastavna sredstva, First Book. Monographs
 

O članku

jezik rada: engleski
vrsta rada: neklasifikovan
DOI: 10.5937/MatMor0401025M
objavljen u SCIndeksu: 02.06.2007.

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