๐ถ-Class ๐น-Contraction in ๐ถโ-Algebra Valued Metric Space
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Published:
Sep 26, 2023
Keywords:
๐ถ-class function ๐ถโ-algebra valued metric space ๐น-contraction
Main Article Content
Abstract
In the present manuscript, we enlarge the class of ๐น-contraction in the framework of ๐ถโ-algebra valued metric space. We present some results on fixed points with the help of ๐ถ-class function for different types of ๐น-contractive condition. The result is an extension and generalization of several metric space results available. Moreover, some examples are presented here to illustrate the usability of obtained results.
Article Details
How to Cite
Dhariwal, R., & Kumar, D. . (2023). ๐ถ-Class ๐น-Contraction in ๐ถโ-Algebra Valued Metric Space. Science & Technology Asia, 28(3), 29โ36. retrieved from https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/248855
Section
Physical sciences
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
References
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Ma Z, Jiang L, Sun H. ๐ถโ-algebra valued metric spaces and related fixed point theorems. Fixed Point Theory and Application 2014, 206. http://www.fixedpointtheoryandapplications.com/content/2014/1/206.
Massit H, Rossafi M. Fixed point theorem for (๐, ๐น)-contraction on ๐ถโ-algebra valued metric spaces. European Journal of Applied Mathematics 2021,1: Article ID 14. https://doi.org/10.28919/ejma.2021.1.14.
Piri H, Rahrovi S, Marasi H, Kumam P. ๐น-contraction on asymmetric metric spaces. Journal of Mathematical and Computational Science 2017อพ17:32-40.
Massit H, Rossafi M, Kabbaj S. Fixed point theorem for (๐, ๐๐น)-contraction on ๐ถโ-algebra valued metric spaces. Asian Journal of Mathematics and Applications 2022, 7. https://www.researchgate.net/publication/358041471.
Ali M U, Kamran T. Multivalued ๐ -contractions and related fixed point theorems with an application. Filomat 2016อพ30:3779-93.
Ali M U, Kamran T, Postolache M. Solution of volterra integral inclusion in ๐-metric spaces via new fixed point theorem. Nonlinear Analysis: Modelling and Control 2017อพ22:17-30.
Altun I, Minak G, Dag H. Multivalued ๐ -contractions on complete metric spaces. Journal of Nonlinear and Convex Analysis 2015อพ16:659 66.
Batra R, Vashistha S. Fixed points of an ๐ -contraction on metric spaces with a graph. International Journal of Computer Mathematics 2014อพ91:2483-90.
Chandok S, Kumar D, Park C. ๐ถโ-algebra valued partial metric space and fixed point theorems. Proceedings of the Indian National Science Academy 2019, 129: Article ID 0037.
Cosentino M, Vetro P. Fixed point results for ๐น-contractive mappings of hardyrogers-type. Filomat 2014อพ28:715-22.
Durmaz G, Minak G, Altun I. Fixed points of ordered ๐น-contractions. Hacettepe Journal of Mathematics and Statistics 2016, 45. https://doi.org/10.15672/HJMS.20164512482.
Klim D, Wardowski D. Fixed points of dynamic processes of set-valued ๐ - contractions and application to functional equations. Fixed Point Theory and Application 2015, 22. https://doi.org/10.1186/s13663-015-0272-y.
Kumar D, Dhariwal R, Park C, Lee J. R.On fixed point in ๐ถโ-algebra valued metric spaces using ๐ถ-class function. International Journal of Nonlinear Analysis and Application 2021อพ12:1157-61.
Mustafa Z, Sims B. A new approach to generalized metric spaces. Journal of Nonlinear and Convex Analysis 2006, 7:289-97.
Nazam M, Arshad M, Postolache M. Coincidence and common fixed point theorems for four mappings satisfying (๐ผ๐ , ๐ )-contraction. Nonlinear Analysis: Modelling and Control 2018อพ23:664-90.
Suzuki T. Fixed point theorems for singlevalued and set-valued ๐ -contractions in ๐-metric spaces. Journal of Fixed Point Theory and Application 2018อพ20:20-35.
Kannan R. Some results on fixed points. Bulletin of the Calcutta Mathematical Society 1968อพ60:71-6.
Chatterjea S K. Fixed-point theorems. Proceedings of the Bulgarian Academy of Sciences 1972อพ25:727-30.
Reich S. Some remarks concerning contraction mappings. Canadian Mathematical Bulletin 1971อพ14:121-4.
Hardy G. E, Rogers T. D. A generalization of a fixed point theoremof Reich. Canadian Mathematical Bulletin 1973อพ16:201-6.
Wardowski D, Dung N.V. Fixed points of ๐ -weak contraction on complete metric spaces. Demonstratio Mathematica 2014, 47. https://doi.org/10.2478 /dema-2014-0012.
Ma Z, Jiang L, Sun H. ๐ถโ-algebra valued metric spaces and related fixed point theorems. Fixed Point Theory and Application 2014, 206. http://www.fixedpointtheoryandapplications.com/content/2014/1/206.
Massit H, Rossafi M. Fixed point theorem for (๐, ๐น)-contraction on ๐ถโ-algebra valued metric spaces. European Journal of Applied Mathematics 2021,1: Article ID 14. https://doi.org/10.28919/ejma.2021.1.14.
Piri H, Rahrovi S, Marasi H, Kumam P. ๐น-contraction on asymmetric metric spaces. Journal of Mathematical and Computational Science 2017อพ17:32-40.
Massit H, Rossafi M, Kabbaj S. Fixed point theorem for (๐, ๐๐น)-contraction on ๐ถโ-algebra valued metric spaces. Asian Journal of Mathematics and Applications 2022, 7. https://www.researchgate.net/publication/358041471.
Ali M U, Kamran T. Multivalued ๐ -contractions and related fixed point theorems with an application. Filomat 2016อพ30:3779-93.
Ali M U, Kamran T, Postolache M. Solution of volterra integral inclusion in ๐-metric spaces via new fixed point theorem. Nonlinear Analysis: Modelling and Control 2017อพ22:17-30.
Altun I, Minak G, Dag H. Multivalued ๐ -contractions on complete metric spaces. Journal of Nonlinear and Convex Analysis 2015อพ16:659 66.
Batra R, Vashistha S. Fixed points of an ๐ -contraction on metric spaces with a graph. International Journal of Computer Mathematics 2014อพ91:2483-90.
Chandok S, Kumar D, Park C. ๐ถโ-algebra valued partial metric space and fixed point theorems. Proceedings of the Indian National Science Academy 2019, 129: Article ID 0037.
Cosentino M, Vetro P. Fixed point results for ๐น-contractive mappings of hardyrogers-type. Filomat 2014อพ28:715-22.
Durmaz G, Minak G, Altun I. Fixed points of ordered ๐น-contractions. Hacettepe Journal of Mathematics and Statistics 2016, 45. https://doi.org/10.15672/HJMS.20164512482.
Klim D, Wardowski D. Fixed points of dynamic processes of set-valued ๐ - contractions and application to functional equations. Fixed Point Theory and Application 2015, 22. https://doi.org/10.1186/s13663-015-0272-y.
Kumar D, Dhariwal R, Park C, Lee J. R.On fixed point in ๐ถโ-algebra valued metric spaces using ๐ถ-class function. International Journal of Nonlinear Analysis and Application 2021อพ12:1157-61.
Mustafa Z, Sims B. A new approach to generalized metric spaces. Journal of Nonlinear and Convex Analysis 2006, 7:289-97.
Nazam M, Arshad M, Postolache M. Coincidence and common fixed point theorems for four mappings satisfying (๐ผ๐ , ๐ )-contraction. Nonlinear Analysis: Modelling and Control 2018อพ23:664-90.
Suzuki T. Fixed point theorems for singlevalued and set-valued ๐ -contractions in ๐-metric spaces. Journal of Fixed Point Theory and Application 2018อพ20:20-35.
Kannan R. Some results on fixed points. Bulletin of the Calcutta Mathematical Society 1968อพ60:71-6.
Chatterjea S K. Fixed-point theorems. Proceedings of the Bulgarian Academy of Sciences 1972อพ25:727-30.
Reich S. Some remarks concerning contraction mappings. Canadian Mathematical Bulletin 1971อพ14:121-4.
Hardy G. E, Rogers T. D. A generalization of a fixed point theoremof Reich. Canadian Mathematical Bulletin 1973อพ16:201-6.
Wardowski D, Dung N.V. Fixed points of ๐ -weak contraction on complete metric spaces. Demonstratio Mathematica 2014, 47. https://doi.org/10.2478 /dema-2014-0012.
