TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Freq.: MONTHLY - Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

New fixed point theorems in dynamic property under rational contractive condition with application

* , , ,

* Corresponding author · click or hover a name for details

pp. 1339–1359Vol. 27Issue 6September 2024DOI: 10.47974/JIM-1783XML
Received:
20 Jan 2023
Published Online:
30 Sep 2024
Article type:
Research Article
Language:
EN
Article no.:
JIM-1783
Pages:
1339–1359

Abstract

In this study, we enhance and generalize multiple findings in the field of fixed point theory within the context of metric spaces. We establish the existence of fixed points for self-maps denoted as A,  provided they meet certain rational contractive criteria. Furthermore, we present dynamic insights that establish connections between these fixed points. We provide illustrative examples that serve to validate the proposed hypotheses. To support our results, we applied our theoretical results in solving a linear congruence problem.

Keywords

Subject Classifications

(2010) 54H2547H10

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). 

Views: 121Downloads: 9Citations: 0