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Related Fixed Point Theorems on Complete and Compact Metric Spaces(PDF)

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

Issue:
1999年04期
Page:
366-369
Research Field:
Publishing date:

Info

Title:
Related Fixed Point Theorems on Complete and Compact Metric Spaces
Author(s):
ZhuShunrong
School of Sciences,NUST,Nanjing 210094
Keywords:
f ix ed points met ric spaces complete met ric spaces compact met ric spaces
PACS:
O177.91
DOI:
-
Abstract:
Fisher B proved the follow ing fixed point theorem: Let ( X , d ) and ( Y, Q) be complete met ric spaces, let T be a cont inuous mapping of X into Y and let S be a mapping of Y into X sat isfying the inequalit ies d( STx , STxc) ≤Cmax { d( x , xc) , d( x , STx ) , d( xc, ST xc) , Q( Tx , Txc) } Q( TSy , TSyc) ≤Cmax{ Q( y , yc) , Q( y , T Sy ) , Q( yc, TSyc) , d ( Sy , Syc) } for all x , xc in X and in Y , where 0 [ C < 1 . Then ST has a unique f ix ed point z in X and TS has a unique f ixed point w in Y . Further, T z = w and Sw = z . T his paper has generalized the result of this theorem and proved two new f ix ed point theorems on complete metric space and compact metric spaces.

References:

1 Fisher B. Related fix ed points on two metric spaces. Math Sem Notes, Kobe Univ 1982, 10, 17~26
2 Fisher B. A fix ed point theor em for compact metric spaces. Publ Math Debrecen, 1978, 25: 193~194

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Last Update: 2013-03-29