Bulletin of Mathematical Analysis and Applications, Volume (8), No (4), Year (2016-11) , Pages (72-77)

#### Title : ( Implicit contractive mappings in sherically complete ultrametric spaces )

Authors: malihe haji mojtahed , Seyyed Alireza Kamel Mirmostafaee ,

Citation: BibTeX | EndNote

#### 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.
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@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.},
}