New fixed point theorems in dynamic property under rational contractive condition with application
*Besma LaouadiCorresponding authorlaouadi.besma@univ-oeb.dzDepartment of Mathematics and InformaticsDynamic Systems and Control LaboratoryLarbi Ben Mhidi UniversityOum El Bouaghi, 4000, AlgeriaView full profile → , Lila Benaouabenaoualeila@gmail.comDepartment of Mathematics and InformaticsDynamic Systems and Control LaboratoryLarbi Ben Mhidi UniversityOum El Bouaghi, 4000, AlgeriaView full profile → , Taki Eddine Oussaeiftaki.oussaeif@univ-oeb.dzDepartment of Mathematics and InformaticsDynamic Systems and Control LaboratoryLarbi Ben Mhidi UniversityOum El Bouaghi, 4000, AlgeriaView full profile → , Xiaolan Liuxiaolanliu@suse.edu.cnAffiliation 1College of Mathematics and StatisticsSichuan University of Science and EngineeringZigong, 643000, ChinaAffiliation 2Key Laboratory of Higher Education of Sichuan Province forEnterprise Informationalization and Internet of ThingsZigong, 643000, ChinaAffiliation 3Center for Applied MathematicsSouth Sichuan, Zigong, 643000, ChinaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 20 Jan 2023
- Published Online:
- 30 Sep 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1783
- Pages:
- 1339–1359
Abstract
Keywords
Subject Classifications
References
[1] B. Alqahtani, A. Fulga, E. Karapinar and V. Rakocevic, Contractions with rational inequalities in the extended b-metric spaces. J. Inequal. Appl. 2019, 220 (2019).
[2] A. Amini-Harandi and A. Petrusel, A fixed point theorem by altering distance technique in complete metric spaces. Miskolc Mathematical Notes, 14(1), 11-17 (2013).
[3] A. C. Aouine and A. Aliouche, Fixed point theorems Of Kannan type With an application to control theory, Applied Mathematics E-Notes 21, 238-249 (2021).
[4] M. Arshad, S. U. Khan and J. Ahmad, Fixed point results for F-contractions involving some new rational expressions. JP Journal of Fixed Point Theory and Applications, 11(1), 79, (2016).
[5] S. Banach, On operations in abstract sets and their applications to integral equations, Fundam. Math. 3, 133-181. (in French) (1922).
[6] K. Berrah, T. E. Oussaeif, and A. Aliouche, Common fixed point theorems of Meir-Keeler contraction type in complex valued metric space and an application to dynamic programming. Journal of Interdisciplinary Mathematics, 25(2), 445-461 (2022).
[7] S. Bhatt, S. Chaukiyal, and R. C. Dimri, Common fixed point of mappings satisfying rational inequality in complex valued matrix space. International Journal of Pure and Applied Mathematics 73(2), 159-164 (2011).
[8] R. T. Bianchini, On a problem of S. Reich concerning the theory of fixed points, Boll. Un.Mat.Ital.5, 103-108. (in Italian) (1972).
[9] S. Chandok, B. S. Choudhury and N. Metiya, Fixed point results in ordered metric spaces for rational type expressions with auxiliary functions. Journal of the Egyptian Mathematical Society, 23(1), 95-101 (2015).
[10] S. Chandok and J. K. Kim, Fixed point theorem in ordered metric spaces for generalized contractions mappings satisfying rational type expressions. J. Nonlinear Funct. Anal. Appl, 17, 301-306 (2012).
[11] S.K. Chatterjea, Fixed-point theorems, C.R.Acad. Bulgare Sci. 25, 727-730 (1972).
[12] B.S. Choudhury, N. Metiya, P. Konar, Fixed point results for rational type contraction in partially ordered complex-valued metric spaces. Bull. Int. Math. Virtual. Inst. 5, 73-80 (2015).
[13] L. B. Ciric, A generalization of Banach’s contraction principle, Proceedings of the American Mathematical society, 45.2 267-273 (1974).
[14] L.B. Ciric, Generalized Contractions and Fixed Point Theorems, Publications of the Institute of Mathematics, 12, 19-26 (1971).
[15] L B. Ciric, On Presic type generalization of the Banach contraction mapping principle. Acta Math. Univ. Comenianae, 76.2, 143-147 (2007).
[16] B.K. Dass and S. Gupta, An extension of Banach contraction principle through rational expressions. Indian J. Pure Appl. Math. 6, 1455-1458 (1975).
[17] P.N. Dutta, B.S. Choudhury, A generalization of contraction principle in metric spaces. Fixed Point Theory and Applications, 1-8 (2008).
[18] M. Frechet, On some points of functional calculus, Rendiconti del Circolo Matematico di Palermo 22, 1-72. (in French) (1906).
[19] H. Huang, Y.M. Singh, M.S. Khan, S. Radenovic, Rational Type Contractions in Extended b-Metric Spaces. Symmetry, 13, 614 (2021).
[20] D. S. Jaggi, Some unique fixed point theorems, Indian J Pure Appl Math, 8, (2), 23-30 (1977).
[21] I. H. Jebril, S. K. Datta, R. Sarkar, and N. Biswas, Common fixed point theorems under rational contractions for a pair of mappings in bicomplex valued metric spaces. Journal of Interdisciplinary Mathematics, 22(7), 1071-1082 (2019).
[22] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 60, 71-76 (1968).
[23] M. S. Khan, A Fixed Point Theorem For Metric Spaces, Rendiconti Dell’ istituto di Mathematica dell’ Universtia di tresti, 8, 69-72 (1976).
[24] F. Khojasteh, M. Abbas and S. Costache, Two new types of fixed point theorems in complete metric spaces. In Abstract and Applied Analysis (2014).
[25] D. Petko Proinov, Fixed point theorems for generalized contractive mappings in metric spaces. Journal of Fixed Point Theory and Applications, 22.1, 1-27 (2020).
[26] H. Piri, S. Rahrovi, P. Kumam, Khan type fixed point theorems in a generalized metric space. J. Math. Computer Sci. 16, 211-217 (2016).
[27] T. Rasham, A. Shoaib, N. Hussain, M. Arshad and S. U. Khan, Common fixed point results for new Ciric-type rational multivalued F-contraction with an application. Journal of Fixed Point Theory and Applications, 20(1), 1-16 (2018).
[28] M. Sarwar, Humaira, H. Huang, Fuzzy fixed point results with rational type contractions in partially ordered complex-valued metric spaces. Commentat. Math. 58, 5-78 (2018).
[29] N. Seshagiri Rao and K. Kalyani, Generalized fixed point results of rational type contractions in partially ordered metric spaces. BMC Research Notes, 14(1), 1-13 (2021).
[30] T. Suzuki, A new type of fixed point theorem in metric spaces. Nonlinear Analysis: Theory, Methods and Applications, 71(11), 5313-5317 (2009).
[31] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl.94 (2012).
[32] M. B. Zada, , M. Sarwar and P. Kumam, Fixed point results of rational type contractions in b-metric spaces. International Journal of Analysis and Applications, 16(6), 904-920 (2018).
