http://hdl.handle.net/20.500.12128/15935
Tytuł: | Generalization of Edelstein's fixed point theorem |
Autor: | Czerwik, Stefan |
Słowa kluczowe: | Edelstein's fixed point theorem; metric spaces |
Data wydania: | 1976 |
Źródło: | Demonstratio Mathematica, Vol. 9, nr 2 (1976) s. 281-285 |
Abstrakt: | Let i = 1 , . . . , n be metric spaces. Let T.,, df i = 1 , . . . , n be transformations mapping of B = X^ * . . . * XQ i n t o X^. itor any p o s i t i v e number a we define (cf. also [3]) Za = »x n ) 6 B s d i ^ i t 1 ! ^ » ' " i x n ) ] < a» i = 1 , . . . , n | . In [ l ] the following f i x e d point theorem has been proved, generalizing the Banach p r i n c i p l e for contraction maps ( c f . [4]): Let E be a metric space and T an operator which transforms E into i t s e l f . Suppose that d[T(x), T(y)] < d(x,y), x ^ y, x,y e E. Assume t h a t there e x i s t s x e E such that the sequence at i t e r a t e s {Tm(x)| contains a subsequence m I T (x)j convergent to a point u e E. Then u is a unique f i x e d point of T. The purpose of the present paper i s to prove (using the n o t a t i o n of t h e s e t s Za„ ) a f i x e d point theorem which generalize s the E d e l s t e i n ' s theorem and the r e s u l t in [5] (Fragment tekstu). |
URI: | http://hdl.handle.net/20.500.12128/15935 |
DOI: | 10.1515/dema-1976-0215 |
ISSN: | 2391-4661 0420-1213 |
Pojawia się w kolekcji: | Artykuły (WNŚiT) |
Plik | Opis | Rozmiar | Format | |
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Czerwik_Generalization_of_Edelsteins.pdf | 407,55 kB | Adobe PDF | Przejrzyj / Otwórz |
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