The <inline-formula> <tex-math notation="LaTeX">$G_M$ </tex-math></inline-formula>-Contraction Principle for Mappings on an <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>-Metric Spaces Endowed With a Graph and Fixed Point Theorems

• Main Authors: Nizar Souayah, Nabil Mlaiki, Mehdi Mrad
• Format: Article
• Language: English
• Published: IEEE 2018-01-01
• Series: IEEE Access
• Subjects: Fixed point; <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">M</italic>-metric spaces; <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">Gm</italic>-contraction; connected graph
• Online Access: https://ieeexplore.ieee.org/document/8356705/

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.