On Some New Results in Graphical Rectangular <i>b</i>-Metric Spaces
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&...
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MDPI AG
2020-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/4/488 |
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doaj-96aeba24d8544e8b959dfb113f0496ec2020-11-25T02:33:48ZengMDPI AGMathematics2227-73902020-04-01848848810.3390/math8040488On Some New Results in Graphical Rectangular <i>b</i>-Metric SpacesPravin Baradol0Jelena Vujaković1Dhananjay Gopal2Stojan Radenović3Department of Mathematics and Humanities, S. V. National Institute of Technology, Surat 395 007, Gujarat, IndiaDepartment of Mathematics, Faculty of Sciences, University in Priština-Kosovska Mitrovica, 38220 Kosovska Mitrovica, SerbiaDepartment of Mathematics and Humanities, S. V. National Institute of Technology, Surat 395 007, Gujarat, IndiaNonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City 700000, VietnamIn 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).https://www.mdpi.com/2227-7390/8/4/488graphical rectangular b-metric spaceBanach G-contractionEdelstein G-contractionMeir–Keeler G-contractionReich G-contraction |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Pravin Baradol Jelena Vujaković Dhananjay Gopal Stojan Radenović |
| spellingShingle |
Pravin Baradol Jelena Vujaković Dhananjay Gopal Stojan Radenović On Some New Results in Graphical Rectangular <i>b</i>-Metric Spaces Mathematics graphical rectangular b-metric space Banach G-contraction Edelstein G-contraction Meir–Keeler G-contraction Reich G-contraction |
| author_facet |
Pravin Baradol Jelena Vujaković Dhananjay Gopal Stojan Radenović |
| author_sort |
Pravin Baradol |
| title |
On Some New Results in Graphical Rectangular <i>b</i>-Metric Spaces |
| title_short |
On Some New Results in Graphical Rectangular <i>b</i>-Metric Spaces |
| title_full |
On Some New Results in Graphical Rectangular <i>b</i>-Metric Spaces |
| title_fullStr |
On Some New Results in Graphical Rectangular <i>b</i>-Metric Spaces |
| title_full_unstemmed |
On Some New Results in Graphical Rectangular <i>b</i>-Metric Spaces |
| title_sort |
on some new results in graphical rectangular <i>b</i>-metric spaces |
| publisher |
MDPI AG |
| series |
Mathematics |
| issn |
2227-7390 |
| publishDate |
2020-04-01 |
| description |
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). |
| topic |
graphical rectangular b-metric space Banach G-contraction Edelstein G-contraction Meir–Keeler G-contraction Reich G-contraction |
| url |
https://www.mdpi.com/2227-7390/8/4/488 |
| work_keys_str_mv |
AT pravinbaradol onsomenewresultsingraphicalrectangularibimetricspaces AT jelenavujakovic onsomenewresultsingraphicalrectangularibimetricspaces AT dhananjaygopal onsomenewresultsingraphicalrectangularibimetricspaces AT stojanradenovic onsomenewresultsingraphicalrectangularibimetricspaces |
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