Some resulte about the restraction of caristies theorem to continiouse function and the contraction property in banach space
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https://doi.org/10.31185/eduj.Vol2.Iss25.2748Keywords:
SomeAbstract
.In this paper ,we show the restriction of Caristi's theorem to contininiouse function can be derived directly from the Zermelo theorem.,on the other hand we consider the completeness and the contraction property in banach space and show that the contraction property implies Lipschitz-completeness or arswise- completeness in a metric spaces .However, in a metric spaces, the contraction property does not imply the usual completeness .Downloads
References
C . Bessaga .(1959), On the converse of the Banach fixed-point principle). Collog . Math . 7,pp (41-43).
Dowing . D and Kirk , W . A.,(1977),(A genera lization of Caristi's theorem with Applications to Non linear Mapping theory ),pacific J .Math .69,pp(339-346) .
Ekeland , I ,(1974),(On the variational brinciple ), J .Math Anal .Appl.47,pp(324-353) .
H .Kneser , (1950) (Eine direkte Ableitung des Zornscheu lemmas aus dem Auswahiaxiomo) .Math . Z.53,PP(110-113).
J .Jachmsk :,(1998) ,(Caristi's fixed point theorem and selections of set-valu contraction) Math .227 , pp(55-67) .
J.Jachymski ,(2003) (Converse to fixed point theorem of Zermelo and Caristi ),Non. Analysis.52,pp(1455-1463).
W. A. Kirk, Caristi fixed point theorem and metric space convexity, Collg. Math. 36(1976),81-86. MR0436111 (55:9061)
S. Leader, Atopological characterization of Banach contractions, Pacific J. Math. 69:2(1977),461-466. MR0436093 (55:9044)
F. Sullivan, A characterization of complete metric space , , Proc. Amer. Math. Soc.83(1981),345-346. MR0624927 (83b:54036).
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