A Generalization of a fixed point theorem of
HONGKUN XU

International Journal of Mathematics Trends and Technology (IJMTT)  
© 2016 by IJMTT Journal  
Volume38 Number1 

Year of Publication : 2016  
Authors : Sujata Goyal 

10.14445/22315373/IJMTTV38P505 
Sujata Goyal "A Generalization of a fixed point theorem of HONGKUN XU", International Journal of Mathematics Trends and Technology (IJMTT). V38(1):2326 October 2016. ISSN:22315373. www.ijmttjournal.org. Published by Seventh Sense Research Group.
Abstract
Xu. H. [1] introduced weakly asymptotic contraction and proved that if T :X X is a continuous map
where (X,d) is a complete metric space and :R R a map ,which is continuous and (s) < s for all s > 0
, (0) = 0 such that given > 0 , there exists n > 0 such that d(T
n
x , T
n
y) (d(x,y)) + , for all x ,
y in X . It is also assumed that some orbit of T i.e. { T
n
x : n N } for some x X is bounded . Then T has a
unique fixed point y in X . Also T
n
x y as n . In this paper ,it has been shown that result is still true if
the function is assumed to be upper semicontinuous.
References
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Keywords
complete metric space, Cauchy sequence, fixed point, continuous map, upper semicontinuous map,
limit superior.