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A New Type of Fixed Point Theorems about Contraction Mapping(PDF)

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

Issue:
1999年05期
Page:
454-457
Research Field:
Publishing date:

Info

Title:
A New Type of Fixed Point Theorems about Contraction Mapping
Author(s):
ZhuShunrong
School of Sciences,NUST,Nanjing 210094
Keywords:
distance fixed-point s metric spaces
PACS:
O177.91
DOI:
-
Abstract:
In the study of f ix ed point theorems, Recent ly Kada et al introduced the concept of w -distance in a met ric space. In this paper the concept of w -distance is int roduced in a complete met ric space and the result is as follows: Let ( X , d ) be a complete metric space and let p be a w -distance in X . Let T : X y X satisfy ing : for all x ∈X , exists n( x )∈N and for all y∈X p ( T n( x ) x , T n( x ) y ) ≤ λmax { p ( x , y ) , p ( x , T n( x ) y ) } , p ( x , T n( x ) x ) and for all u I X , u X Tu , inf { p ( x , u) + p ( x , Tix ) : x∈ X } > 0, i∈N T hen T has a unique f ix ed point in X and p ( y , y ) = 0 。

References:

1 Kada O, Suzuki T, Takahashi W. Nonconvex minimization theor ems and fix ed point theorems in complete metric spaces1Math Japanica, 1996, 44: 381~ 391
2 Kannan R. Some results on fix ed points. Amer Math Monthly , 1969, 76: 405~ 408

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Last Update: 2013-03-29