Results for Coupled Fixed Point in Partial Metric Spaces via Contractive Type Condition Involving Rational Term

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Authors

  • G. S. Saluja
     H.N. 3/1005, Geeta Nagar, Raipur - 492001 (C.G.) ,IN

DOI:

https://doi.org/10.18311/jims/2024/32264

Keywords:

Coupled Fixed Point, Contractive Type Condition Involving Rational Term, Control Function, Partial Metric Space.

Abstract

The purpose of this paper is to establish a coupled fixed point theorem for contractive type condition involving rational term in the setting of partial metric spaces using control function. Furthermore, we provide some consequences of the established result. We demonstrate that the coupled fixed point problem of the aforementioned result is well-posed. Our results extend and generalize several previously published results from the existing literature.

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Published

2024-07-01

How to Cite

Saluja, G. S. (2024). Results for Coupled Fixed Point in Partial Metric Spaces via Contractive Type Condition Involving Rational Term. The Journal of the Indian Mathematical Society, 91(3-4), 426–445. https://doi.org/10.18311/jims/2024/32264

Issue

Volume 91, Issue 3-4, July-December 2024

Section

Articles

License

Copyright (c) 2024 Gurucharan Singh Saluja

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2022-12-29
Accepted 2023-07-23
Published 2024-07-01

 

References

M. Abbas, M. Ali Khan and S. Radenovi´c, Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl. Math. Comput., 217. (2010), 195 - 202.

R. Alsubaie, B. Alqahtani, E. Karapinar and A. F. Rold´an L´opez de Hierro, Extended simulation function via rational expressions, Mathematics, 8. (5) (2020), 710, https://doi.org/10.3390/math8050710.

I. Altun, F. Sola and H. Simsek, Generalized contractions on partial metric spaces, Topology and its Appl., 157. (2010), 2778 - 2785.

H. Aydi, Some coupled fixed point results on partial metric spaces, International J. Math. Math. Sci., 2011, Article ID 647091, 11 pages.

H. Aydi, M. Abbas and C. Vetro, Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric spaces, Topology and Its Appl., 159. (14) (2012), 3234 - 3242.

T. G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis: TMA, 65. (7) (2006), 1379 - 1393.

S. Chandok, D. Kumar and M. S. Khan, Some results in partial metric space using auxiliary functions, Applied Math. E-Notes, 15. (2015), 233 - 242.

L. Ciric and V. Lakshmikantham, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis: TMA, 70. (12) (2009), 4341 - 4349.

B. K. Dass and S. Gupta, An extension of Banach contraction principle through rational expression, Indian J. Pure Appl. Math., 6. (1975), 1455 - 1458.

R. Heckmann, Approximation of metric spaces by partial metric spaces, Appl. Categ. Structures, 7. (1-2), (1999), 71 - 83.

D. S. Jaggi, Some unique fixed point theorems, Indian J. Pure Appl. Math., 8. (1977), 223 - 230.

E. Karapinar, W. Shatanawi and K. Tas, Fixed point theorems on partial metric spaces involving rational expressions, Miskolc Math. Notes, 14. (2013), 135 - 142.

E. Karapinar, Rational forms that imply the uniqueness of fixed points in partial metric spaces, J. Nonlinear Convex Anal., 20. (10), (2019), 2171 - 2186.

E. Karapinar, A note on a rational form contractions with discontinuties at fixed points, Fixed Point Theory, 21. (1), (2020), 211 - 220. doi:10.24193/fpt.ro.2020.1.15.

E. Karapinar, A. Atangana and A. Fulga, Pata type contractions involving rational expressions with an application to integral equations, Discrete and Continuous Dynamical Systeme-S, 14. (10), (2020), 3629 - 3640. doi:10.3934/dcdss.2020420.

E. Karapinar, Chi-Ming Chen, M. A. Alghamdi and A. Fulga, Advances on the fixed point results via simulation function involving rational terms, Advances in Difference Equations, 2021, Article ID 2021:409.

J. K. Kim and S. Chandok, Coupled common fixed point theorems for generalized nonlinear contraction mappings with the mixed monotone property in partially ordered metric spaces, Fixed Point Theory Appl., (2013), 2013:307.

J. K. Kim, G. A. Okeke and W. H. Lim, Common coupled fixed point theorems for w-compatible mappings in partial metric spaces, Global J. Pure Appl. Math., 13. (2), (2017), 519 - 536.

S. G. Matthews, Partial metric topology, Research report 2012, Deptt. Ccmputer Science, University of Warwick, 1992.

S. G. Matthews, Partial metric topology, Proceedings of the 8th summer conference on topology and its applications, Annals of the New York Academy of Sciences, 728. (1994), 183 - 197.

R. Pant, R. Shukla, H. K. Nashine and R. Panicker, Some new fixed point theorems in partial metric spaces with applications, J. Function spaces, 2017, Article ID 1072750, 13 pages.

S. Reich and A. J. Zaslavski, Well posedness of fixed point problem, Far East J. Math., special volume part III, (2001), 393 - 401.

F. Sabetghadam, H. P. Mashiha and A. H. Sanatpour, Some coupled fixed point theorems in cone metric spaces, Fixed Point Theory Appl., (2009), Article ID 125426, 8 pages.