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

Sujata Goyal

doi:https://doi.org/10.14445/22315373/IJMTT-V38P505

International Journal of Mathematics Trends and Technology

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Volume 38 | Number 1 | Year 2016 | Article Id. IJMTT-V38P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V38P505

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

Sujata Goyal

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.

Keywords

complete metric space, Cauchy sequence, fixed point, continuous map, upper semicontinuous map, limit superior.

References

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Citation :

Sujata Goyal, "A Generalization of a fixed point theorem of HONG-KUN XU," International Journal of Mathematics Trends and Technology (IJMTT), vol. 38, no. 1, pp. 23-26, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V38P505