Some Fixed Point Results on Generalized Weak Contractions in Partial Metric Spaces With an Application

Authors

DOI:

https://doi.org/10.26713/cma.v15i2.2610

Keywords:

Generalized \(\tau\)-\(\psi\)-\(\varphi\) weak contraction mapping, \(\tau\)-\(\varphi\) Weak contraction mapping, Partial metric space

Abstract

In this paper, we consider generalized \(\tau\)-\(\psi\)-\(\varphi\) weak contraction and generalized \(\tau\)-\(\varphi\) weak contraction mappings in the setting of partial metric spaces and verify the existence of a fixed point on such spaces. Our results extend and strengthen various known results in this direction. We present an example showing the significance of our result. We also show that our result can be applied to the existence of solutions of a differential equation.

Downloads

Download data is not yet available.

References

Y. I. Alber and S. Guerre-Delabrieer, Principles of weakly contractive maps in Hilbert spaces, in: New Results in Operator Theory and Its Applications. Operator Theory: Advances and Applications, I. Gohberg and Y. Lyubich (editors), Vol. 98, Birkhäuser, Basel (1997), DOI: 10.1007/978-3-0348-8910-0_2.

A. Baiz, J. Mouline and A. Kari, Fixed point theorems for generalized τ-ψ-contraction mappings in rectangular quasi b-metric spaces, Advances in Fixed Point Theory 13 (2023), Article ID 10, DOI: 10.28919/afpt/8114.

A. Baiz, J. Mouline, Y. E. Bekri, A. Faiz and K. Bouzkoura, New fixed point theorems for τ-ψ-contraction mappings in complete rectangular M-metric space, Advances in Fixed Point Theory 13 (2023), Article ID 18, DOI: 10.28919/afpt/8190.

S. Chandok, D. Kumar and M. S. Khan, Some results in partial metric space using auxiliary functions, Applied Mathematics E-Notes 15 (2015), 233 – 242, URL: https://www.emis.de/journals/AMEN/2015/AMEN-150228.pdf.

D. Ðukic, Z. Kadelburg and S. Radenovic, Fixed points of Geraghty-type mappings in various generalized metric spaces, Abstract and Applied Analysis 2011 (2011), 561245, 13 pages, DOI: 10.1155/2011/561245.

P. N. Dutta and B. S. Choudhury, A generalisation of contraction principle in metric spaces, Fixed Point Theory and Applications 2008 (2008), Article number 406368, DOI: 10.1155/2008/406368.

E. Karapınar, L. Gholizadeh, H. Alsulami and M. Noorwali, α-(ψ-ϕ) Contractive mappings on quasi-partial metric spaces, Fixed Point Theory and Applications 2015 (2015), Article number 105, DOI: 10.1186/s13663-015-0352-z.

E. Karapınar, W. Shatanawi and K. Tas, Fixed point theorem on partial metric spaces involving rational expressions, Miskolc Mathematical Notes, 14(1) (2013), 135 – 142, DOI: 10.18514/MMN.2013.471.

M. S. Khan, M. Swaleh and S. Sessa, Fixed point theorems by altering distances between the points, Bulletin of the Australian Mathematical Society 30(1) (1984), 1 – 9, DOI: 10.1017/S0004972700001659.

P. Kumam, C. Vetro and F. Vetro, Fixed points for weak α-ψ-contractions in partial metric spaces, Abstract and Applied Analysis 2013 (2013), 986028, 9 pages, DOI: 10.1155/2013/986028.

S. G. Matthews, Partial metric topology, Annals of the New York Academy of Sciences 728 (1994), 183 – 197, DOI: 10.1111/j.1749-6632.1994.tb44144.x.

S. G. Matthews, Partial metric topology, Research Report 2012, Department of Computer Science, University of Warwick, UK (1992).

A. A. Mebawondu and S. I. Mebawondu, Generalized Suzuki (ψ,ϕ)-contraction in complete metric spaces, International Journal of Nonlinear Analysis and Applications 12(1) (2021), 963 – 978, DOI: 10.22075/ijnaa.2020.15983.1837.

M. Nazam, M. Arshad and C. Park, Fixed point theorems for improved α-Geraghty contractions in partial metric spaces, Journal of Nonlinear Sciences and Applications 9(6) (2016), 4436 – 4449, DOI: 10.22436/jnsa.009.06.83.

B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Analysis: Theory, Methods & Applications 47(4) (2001), 2683 – 2693, DOI: 10.1016/S0362-546X(01)00388-1.

B. Samet, C. Vetro and P. Vetro, Fixed point theorem for α-ψ contractive type mappings, Nonlinear Analysis: Theory, Methods & Applications 75(4) (2012), 2154 – 2165, DOI: 10.1016/j.na.2011.10.014.

I. Yildirim, A. H. Ansari, M. S. Khan and B. Fisher, Fixed point theorems on partial metric spaces involving rational type expressions with C-class functions, Turkish Journal of Mathematics and Computer Science 7 (2017), 1 – 9, URL: https://dergipark.org.tr/en/pub/tjmcs/issue/31829/313306.

Downloads

Published

14-11-2024
CITATION

How to Cite

Tiwari, H., & Padmavati. (2024). Some Fixed Point Results on Generalized Weak Contractions in Partial Metric Spaces With an Application. Communications in Mathematics and Applications, 15(2), 605–618. https://doi.org/10.26713/cma.v15i2.2610

Issue

Vol. 15 No. 2 (2024)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.