# Fixed point theorems of $G$-fuzzy contractions in fuzzy metric spaces endowed with a graph

• Volume: 22, Issue: 1, page 1-12
• ISSN: 1804-1388

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## Abstract

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Let $\left(X,M,*\right)$ be a fuzzy metric space endowed with a graph $G$ such that the set $V\left(G\right)$ of vertices of $G$ coincides with $X$. Then we define a $G$-fuzzy contraction on $X$ and prove some results concerning the existence and uniqueness of fixed point for such mappings. As a consequence of the main results we derive some extensions of known results from metric into fuzzy metric spaces. Some examples are given which illustrate the results.

## How to cite

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Shukla, Satish. "Fixed point theorems of $G$-fuzzy contractions in fuzzy metric spaces endowed with a graph." Communications in Mathematics 22.1 (2014): 1-12. <http://eudml.org/doc/261961>.

@article{Shukla2014,
abstract = {Let $(X,M,\ast )$ be a fuzzy metric space endowed with a graph $G$ such that the set $V(G)$ of vertices of $G$ coincides with $X$. Then we define a $G$-fuzzy contraction on $X$ and prove some results concerning the existence and uniqueness of fixed point for such mappings. As a consequence of the main results we derive some extensions of known results from metric into fuzzy metric spaces. Some examples are given which illustrate the results.},
author = {Shukla, Satish},
journal = {Communications in Mathematics},
keywords = {graph; partial order; fuzzy metric space; contraction; fixed point; graph; partial order; fuzzy metric space; contraction; fixed point},
language = {eng},
number = {1},
pages = {1-12},
publisher = {University of Ostrava},
title = {Fixed point theorems of $G$-fuzzy contractions in fuzzy metric spaces endowed with a graph},
url = {http://eudml.org/doc/261961},
volume = {22},
year = {2014},
}

TY - JOUR
AU - Shukla, Satish
TI - Fixed point theorems of $G$-fuzzy contractions in fuzzy metric spaces endowed with a graph
JO - Communications in Mathematics
PY - 2014
PB - University of Ostrava
VL - 22
IS - 1
SP - 1
EP - 12
AB - Let $(X,M,\ast )$ be a fuzzy metric space endowed with a graph $G$ such that the set $V(G)$ of vertices of $G$ coincides with $X$. Then we define a $G$-fuzzy contraction on $X$ and prove some results concerning the existence and uniqueness of fixed point for such mappings. As a consequence of the main results we derive some extensions of known results from metric into fuzzy metric spaces. Some examples are given which illustrate the results.
LA - eng
KW - graph; partial order; fuzzy metric space; contraction; fixed point; graph; partial order; fuzzy metric space; contraction; fixed point
UR - http://eudml.org/doc/261961
ER -

## References

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