𝐶-Class 𝐹-Contraction in 𝐶∗-Algebra Valued Metric Space
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已出版:
9月 26, 2023
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摘要
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.
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Dhariwal, R., & Kumar, D. . (2023). 𝐶-Class 𝐹-Contraction in 𝐶∗-Algebra Valued Metric Space. Science & Technology Asia, 28(3), 29–36. 取读于 从 https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/248855
栏目
Physical sciences
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参考
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.
