The  $G_M$ -Contraction Principle for Mappings on an  $M$ -Metric Spaces Endowed With a Graph and Fixed Point Theorems | Zendy

Nizar Souayah | Zendy; Nabil Mlaiki | Zendy; Mehdi Mrad | Zendy

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The

$G_M$

-Contraction Principle for Mappings on an

$M$

-Metric Spaces Endowed With a Graph and Fixed Point Theorems

Author(s) -

Nizar Souayah,

Nabil Mlaiki,

Mehdi Mrad

Publication year - 2018

Publication title -

ieee access

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.587

H-Index - 127

ISSN - 2169-3536

DOI - 10.1109/access.2018.2833147

Subject(s) - aerospace , bioengineering , communication, networking and broadcast technologies , components, circuits, devices and systems , computing and processing , engineered materials, dielectrics and plasmas , engineering profession , fields, waves and electromagnetics , general topics for engineers , geoscience , nuclear engineering , photonics and electrooptics , power, energy and industry applications , robotics and control systems , signal processing and analysis , transportation

Fixed point theory is a very important tool in mathematics and applied sciences. Latterly, many application examples have been presented for communication network and computer science fields. The proposed schema can be considered as a theoretical foundation for such a type of applications. In this paper, we introduce the notion of the G_m-contraction to generalize and extend the notion of G-contraction. We investigate the existence and uniqueness of the fixed point for such contractions in M-metric space endowed with a graph. Our results extend and generalize various results in the existing literature, in particular the results of Jachymski. Some examples are included, which illustrate the results proved herein.

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