Fixed point theorems in extended b metric space based on rational contraction
Abstract
In this paper, we use rational type contraction for two self-mappings to prove popular fixed-point theorems in extended complete b-metric spaces. The results demonstrated by Mlaiki et al. for a single self-mapping in extended complete b-metric space are improved and expanded by our research. Without assuming that any mapping is continuous, we generalize their findings for two self-mappings.
How to Cite This Article
Shilpa Rathore, Dr. Abha Tenguria (2025). Fixed point theorems in extended b metric space based on rational contraction . International Journal of Multidisciplinary Research and Growth Evaluation (IJMRGE), 6(6), 801-805. DOI: https://doi.org/10.54660/IJMRGE.2025.6.6.801-805
References
- 1. Mlaiki N, Shah SK, Sarwar M. Rational-typecontractionsandtheirapplicationsinextendedb-metricspaces. Resultsin Controland Optimization.2024;16:111.
- 2. Banach S. Surlesop?rationsdanslesensemblesabstraitsetleursapplicationsaux?quationsint?grales. Fundamenta Mathematicae.1922;3:133181.
- 3. Bourbaki N. Topologie G?n?rale. Paris: Hermann;1974.
- 4. Bakhtin IA. Thecontractionmappingprincipleinalmostmetricspaces. Functional Analysis, Unianowsk Gos Ped Inst.1989;30:2637.
- 5. Czerwik S. Contractionmappingsinb-metricspaces. Acta Mathematicaet Informatica Universitatis Ostraviensis.1993;1:511.
- 6. Kir M, Kiziltun?H. Onsomewell-knownfixedpointtheoremsinb-metricspace. Turkish Journalof Analysisand Number Theory.2013;1:1316.
- 7. Boriceanu M. Fixedpointtheoryformultivaluedgeneralizedcontractiononasetwithtwob-metrics. Studia Universitatis-Bolyai, Mathematica.2009;3:114.
- 8. Bota M, Molnar A, Varga C. On Ekeland'svariationalprincipleinb-metricspaces. Fixed Point Theory.2011;12(2\:2128.
- 9. Pacurar M. Sequencesofalmostcontractionsandfixedpointsinb-m-137.
- 10. Fagin R, Stockmeyer L. Relaxingthetriangleinequalityinpatternmatching. International Journalof Computer Vision.1998;30:219231.
- 11. Kamran T, Samreen M, Ain QU. Ageneralizationofb-metricspaceandsomefixedpointtheorems. Mathematics(MDPI\.2017;5(19\:17.12.-metricspace. Journalof Inequalitiesand Applications.2019;2019:113.
- 13. Shatanawi W, Shatnawi TA. Somefixedpointresultsbasedoncontractionsofnewtypesforextendedb-metricspaces. AIMSMathematics.2023;8(5\:1092910946.
- 14. Kadak U. Ontheclassicalsetsofsequenceswithfuzzyb-metric. General Mathematics Notes.2014;23:21992184.