On Some New Results in Graphical Rectangular <i>b</i>-Metric Spaces

• Main Authors: Pravin Baradol, Jelena Vujaković, Dhananjay Gopal, Stojan Radenović
• Format: Article
• Language: English
• Published: MDPI AG 2020-04-01
• Series: Mathematics
• Subjects: graphical rectangular b-metric space; Banach G-contraction; Edelstein G-contraction; Meir–Keeler G-contraction; Reich G-contraction
• Online Access: https://www.mdpi.com/2227-7390/8/4/488
• ISSN: 2227-7390

In this paper, we provide an approach to establish the Banach contraction principle <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>for</mi> <mspace width="4.pt"></mspace> <mi>the</mi> <mspace width="4.pt"></mspace> <mi>case</mi> <mspace width="3.33333pt"></mspace> <mi>λ</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>, Edelstein, Reich, and Meir–Keeler type contractions in the context of graphical rectangular <i>b</i>-metric space. The obtained results not only enrich and improve recent fixed point theorems of this new metric spaces but also provide positive answers to the questions raised by Mudasir Younis et al. (J. Fixed Point Theory Appl., doi:10.1007/s11784-019-0673-3, 2019).