A Generalization of a fixed point theorem of HONG-KUN XU

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2016 by IJMTT Journal
Volume-38 Number-1
Year of Publication : 2016
Authors : Sujata Goyal
  10.14445/22315373/IJMTT-V38P505

MLA

Sujata Goyal "A Generalization of a fixed point theorem of HONG-KUN XU", International Journal of Mathematics Trends and Technology (IJMTT). V38(1):23-26 October 2016. ISSN:2231-5373. 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.