Title : ( Implicit contractive mappings in sherically complete ultrametric spaces )
Authors: malihe haji mojtahed , Seyyed Alireza Kamel Mirmostafaee ,
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Abstract
In this paper, we apply implicit functions to establish a general fixed point theorem in spherically complete ultrametric spaces which enable us to extend some known results. In particular, we will show that in a spherically complete space $X$ a self-mapping $T$ satisfies $$d(Tx, Ty) < \max \lbrace d(x, Tx), d(y, Ty), d(x, Ty), d(y, Tx), d(x, y) \rbrace$$ for each $x, y \in X$ with $x \neq y$, then $T$ has a unique fixed point. This improves Gajic's fixed point theorem in spherically complete ultrametric spaces.
Keywords
, Fixed points, contractions, implicit functions, ultrametric spaces.
@article{paperid:1060168,
author = {Haji Mojtahed, Malihe and Kamel Mirmostafaee, Seyyed Alireza},
title = {Implicit contractive mappings in sherically complete ultrametric spaces},
journal = {Bulletin of Mathematical Analysis and Applications},
year = {2016},
volume = {8},
number = {4},
month = {November},
issn = {1821-1291},
pages = {72--77},
numpages = {5},
keywords = {Fixed points; contractions; implicit functions; ultrametric spaces.},
}
%0 Journal Article
%T Implicit contractive mappings in sherically complete ultrametric spaces
%A Haji Mojtahed, Malihe
%A Kamel Mirmostafaee, Seyyed Alireza
%J Bulletin of Mathematical Analysis and Applications
%@ 1821-1291
%D 2016
