𝐶-Class 𝐹-Contraction in 𝐶∗-Algebra Valued Metric Space
Keywords:
𝐶-class function, 𝐶∗-algebra valued metric space, 𝐹-contractionAbstract
In the present manuscript, we enlarge the class of 𝐹-contraction in the framework of 𝐶∗-algebra valued metric space. We present some results on fixed points with the help of 𝐶-class function for different types of 𝐹-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.
References
Banach S. Sur les op´𝑒rations dans les ensembles abstraits et leur application aux ´𝑒quations int´𝑒grales. Fundamenta Mathematicae 1922, 3:133-81.
Ma Z, Jiang L, Sun H. 𝐶∗-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 (𝜙, 𝐹)-contraction on 𝐶∗-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. 𝐹-contraction on asymmetric metric spaces. Journal of Mathematical and Computational Science 2017;17:32-40.
Massit H, Rossafi M, Kabbaj S. Fixed point theorem for (𝜙, 𝑀𝐹)-contraction on 𝐶∗-algebra valued metric spaces. Asian Journal of Mathematics and Applications 2022, 7. https://www.researchgate.net/publication/358041471.
Ali M U, Kamran T. Multivalued 𝑓 -contractions and related fixed point theorems with an application. Filomat 2016;30:3779-93.
Ali M U, Kamran T, Postolache M. Solution of volterra integral inclusion in 𝑏-metric spaces via new fixed point theorem. Nonlinear Analysis: Modelling and Control 2017;22:17-30.
Altun I, Minak G, Dag H. Multivalued 𝑓 -contractions on complete metric spaces. Journal of Nonlinear and Convex Analysis 2015;16:659 66.
Batra R, Vashistha S. Fixed points of an 𝑓 -contraction on metric spaces with a graph. International Journal of Computer Mathematics 2014;91:2483-90.
Chandok S, Kumar D, Park C. 𝐶∗-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 𝐹-contractive mappings of hardyrogers-type. Filomat 2014;28:715-22.
Durmaz G, Minak G, Altun I. Fixed points of ordered 𝐹-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 𝑓 - 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 𝐶∗-algebra valued metric spaces using 𝐶-class function. International Journal of Nonlinear Analysis and Application 2021;12:1157-61.
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 (𝛼𝑠, 𝑓 )-contraction. Nonlinear Analysis: Modelling and Control 2018;23:664-90.
Suzuki T. Fixed point theorems for singlevalued and set-valued 𝑓 -contractions in 𝑏-metric spaces. Journal of Fixed Point Theory and Application 2018;20:20-35.
Kannan R. Some results on fixed points. Bulletin of the Calcutta Mathematical Society 1968;60:71-6.
Chatterjea S K. Fixed-point theorems. Proceedings of the Bulgarian Academy of Sciences 1972;25:727-30.
Reich S. Some remarks concerning contraction mappings. Canadian Mathematical Bulletin 1971;14:121-4.
Hardy G. E, Rogers T. D. A generalization of a fixed point theoremof Reich. Canadian Mathematical Bulletin 1973;16:201-6.
Wardowski D, Dung N.V. Fixed points of 𝑓 -weak contraction on complete metric spaces. Demonstratio Mathematica 2014, 47. https://doi.org/10.2478 /dema-2014-0012.
Ma Z, Jiang L, Sun H. 𝐶∗-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 (𝜙, 𝐹)-contraction on 𝐶∗-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. 𝐹-contraction on asymmetric metric spaces. Journal of Mathematical and Computational Science 2017;17:32-40.
Massit H, Rossafi M, Kabbaj S. Fixed point theorem for (𝜙, 𝑀𝐹)-contraction on 𝐶∗-algebra valued metric spaces. Asian Journal of Mathematics and Applications 2022, 7. https://www.researchgate.net/publication/358041471.
Ali M U, Kamran T. Multivalued 𝑓 -contractions and related fixed point theorems with an application. Filomat 2016;30:3779-93.
Ali M U, Kamran T, Postolache M. Solution of volterra integral inclusion in 𝑏-metric spaces via new fixed point theorem. Nonlinear Analysis: Modelling and Control 2017;22:17-30.
Altun I, Minak G, Dag H. Multivalued 𝑓 -contractions on complete metric spaces. Journal of Nonlinear and Convex Analysis 2015;16:659 66.
Batra R, Vashistha S. Fixed points of an 𝑓 -contraction on metric spaces with a graph. International Journal of Computer Mathematics 2014;91:2483-90.
Chandok S, Kumar D, Park C. 𝐶∗-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 𝐹-contractive mappings of hardyrogers-type. Filomat 2014;28:715-22.
Durmaz G, Minak G, Altun I. Fixed points of ordered 𝐹-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 𝑓 - 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 𝐶∗-algebra valued metric spaces using 𝐶-class function. International Journal of Nonlinear Analysis and Application 2021;12:1157-61.
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 (𝛼𝑠, 𝑓 )-contraction. Nonlinear Analysis: Modelling and Control 2018;23:664-90.
Suzuki T. Fixed point theorems for singlevalued and set-valued 𝑓 -contractions in 𝑏-metric spaces. Journal of Fixed Point Theory and Application 2018;20:20-35.
Kannan R. Some results on fixed points. Bulletin of the Calcutta Mathematical Society 1968;60:71-6.
Chatterjea S K. Fixed-point theorems. Proceedings of the Bulgarian Academy of Sciences 1972;25:727-30.
Reich S. Some remarks concerning contraction mappings. Canadian Mathematical Bulletin 1971;14:121-4.
Hardy G. E, Rogers T. D. A generalization of a fixed point theoremof Reich. Canadian Mathematical Bulletin 1973;16:201-6.
Wardowski D, Dung N.V. Fixed points of 𝑓 -weak contraction on complete metric spaces. Demonstratio Mathematica 2014, 47. https://doi.org/10.2478 /dema-2014-0012.
Downloads
Published
2023-09-26
How to Cite
Dhariwal, R., & Kumar, D. . (2023). 𝐶-Class 𝐹-Contraction in 𝐶∗-Algebra Valued Metric Space. Science & Technology Asia, 28(3), 29–36. Retrieved from https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/248855
Issue
Section
Physical sciences
License
Copyright (c) 2023 Science & Technology Asia
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
