Some results in the new direction of multiplicative metric space
Abstract
Inspired by the recent work of Stojan Radenovi\'c and Bessem Samet \cite{stojan new direction}, we prove some fixed point theorems in multiplicative metric space which are not equivalent to the corresponding theorems in standard metric space using the function \(\varphi : [1, \infty) \to [0, \infty)\) that satisfies the condition:
$
\varphi(s) \geq b (\ln s)^c, s > 1,
$
where \(b\) and \(c\) are positive constants. We give an application in boundary value problem for the second-order differential
equation to validate our results.
Downloads
References
R. P. Agarwal, E. Karapinar and B. Samet, An essential remark on fixed point results on multiplicative metric spaces, Fixed Point Theory and Applications, 2016 (2016), 21.
S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fundamenta Mathematicae, 3 (1922), 133–181.
A. E. Bashirov, E. M. Kurpınar and A. Ozyapıcı, Multiplicative calculus and its applications, Journal of Mathematical Analysis and Applications, 337 (2008), 36–48.
T. Dosenovic, M. Postolache and S. Radenovic, On multiplicative metric spaces: survey, Fixed Point Theory and Applications, 2016 (2016), 1–17.
M. Geraghty, On contractive mappings, Proceedings of the American Mathematical Society, 40 (1973), 604–608.
M. Grossman and R. Katz, Non-Newtonian Calculus, Lee Press, Pigeon Cove, 1972.
R. Kannan, Some results on fixed points, Bulletin of the Calcutta Mathematical Society, 10 (1968), 71–76.
M. Ozav¸sar and A. C. C¸ evikel, Fixed point of multiplicative contraction mappings on multiplicative metric spaces, Journal of Engineering Technology and Applied Sciences, 2 (2017), 65–79.
S. Radenovic and B. Samet, New directions in fixed point theory in multiplicative metric spaces, Filomat, 39(9) (2025), 3083–3097.
S. Reich, Some remarks concerning contraction mappings, Canadian Mathematical Bulletin, 14 (1971), 121–124.
S. Shukla, Some critical remarks on the multiplicative metric spaces and fixed point results, Journal of Advanced Mathematical Studies, 9(3) (2016), 454–458.
I. Shashikanta, Y. Mahendra, G. A. Hirankumar and A. Moussaoui A New Interpolative (φ, ψ)-Type Z-Contraction with Application to Nonlinear Matrix Equation Systems, Boletim da Sociedade Paranaense de Matematica, 43 (2025).
Copyright (c) 2025 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
