$\varphi$-FIXED POINT RESULTS IN METRIC SPACES WITH AN APPLICATION
Keywords:
metric space, $\varphi$-fixed $\left(\mathcal{F}^{\#}, \varphi\right)$-contraction, differential equationDOI:
https://doi.org/10.17654/0972087125013Abstract
In this article, we present $\varphi$-fixed point results using $\left(\mathcal{F}^{\#}, \varphi\right)$ contraction in metric spaces, thereby deriving several corollaries from established results. We provide appropriate non-trivial examples to substantiate the derived results, which have been verified through program codes and graphically explained. Additionally, these results have been applied to find analytical solutions to boundary value problems.
Received: April 2, 2025
Accepted: April 24, 2025
References
S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math. 3(1) (1922), 133-181.
S. C. Nesic, A theorem on contractive mappings, Mat. Vesnik 44 (1992), 51-54.
P. P. Murthy, Y. J. Cho and B. Fisher, Common fixed points of Gregus type mappings, Glas. Mat. Ser. III 30(50) (1995), 335-341.
S. N. Lal, P. P. Murthy and Y. J. Cho, An extension of Telci, Tas and Fisher’s theorem, J. Korean Math. Soc. 33(4) (1996), 891-908.
W. Kirk and N. Shahzad, Fixed Point Theory in Distance Spaces, Springer International Publishing, Switzerland, 2014.
D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012(1) (2012), 1-6.
P. Debnath, N. Konwar and S. Radenovic, Metric Fixed Point Theory, Applications in Science, Engineering and Behavioural Sciences, Springer, 2021.
M. Jleli, B. Samet and C. Vetro, Fixed point theory in partial metric spaces via -fixed point’s concept in metric spaces, J. Inequal. Appl. 2014(1) (2014), 1-9.
N. Fabiano, Z. Kadelburg, N. Mirkov, V. S. Cavi and S. Radenovic, On F-contractions: a survey, Contemp. Math. 3(3) (2022), 327.
H. N. Saleh, M. Imdad and W. M. Alfaqih, Some metrical -fixed point results of Wardowski type with applications to integral equations, Bol. Soc. Parana. Mat. (3) 40 (2022), 1-11.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA

This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________
Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
Contact Puspha Publishing House for more info or permissions.





