A Study of Coupled Fixed Point in Multiplicative S-Metric Space

Authors

DOI:

https://doi.org/10.26713/cma.v15i3.2779

Keywords:

Coupled fixed point, Compatible mappings, Multiplicative S-metric space

Abstract

This study presents a novel common coupled fixed point result for two mappings in multiplicative S-metric space. Uniqueness of this point is proven through the utilization of a compatibility condition, validated through a provided example. Additionally, an application to integral equations is discussed within this article.

Downloads

References

M. Abbas, M. A. Khan and S. Redenovi´c, Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Applied Mathematics and Computation 217(1) (2010), 195 – 202, DOI: 10.1016/j.amc.2010.05.042.

H. Aydi, B. Samet and C. Vetro, Coupled fixed point results in cone metric spaces for w-compatible mappings, Fixed Point Theory and Applications 2011 (2011), Article number: 27, DOI: 10.1186/1687-1812-2011-27.

S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae 3(1) (1922), 133 – 181, URL: https://eudml.org/doc/213289.

T. G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis: Theory, Methods & Applications 65(7) (2006), 1379 – 1393, DOI: 10.1016/j.na.2005.10.017.

C. Chifu and G. Petrusel, New results on coupled fixed point theory in metric spaces endowed with a directed graph, Fixed Point Theory and Applications 2014 (2014), Article number: 151, DOI: 10.1186/1687-1812-2014-151.

Y. J. Cho, M. H. Shah and N. Hussain, Coupled fixed points of weakly F-contractive mappings in topological spaces, Applied Mathematics Letters 24(7) (2011), 1185 – 1190, DOI: 10.1016/j.aml.2011.02.004.

D. Ðori´c, Z. Kadelburg and S. Radenovi´c, Coupled fixed point results for mappings without mixed monotone property, Applied Mathematics Letters 25(11) (2012), 1803 – 1804, DOI: 10.1016/j.aml.2012.02.022.

M. Gandhi and A. Aserkar, Coupled fixed point theorem in quasi metric space, Italian Journal of Pure and Applied Mathematics 47 (2022), 449 – 457, URL: https://ijpam.uniud.it/online_issue/202247/30%20Gandhi-Aserkar.pdf.

F. Gu, Some new common coupled fixed point results in two generalized metric spaces, Fixed Point Theory and Applications 2013 (2013), Article number: 181, DOI: 10.1186/1687-1812-2013-181.

X. He, M. Song and D. Chen, Common fixed points for weak commutative mappings on a multiplicative metric space, Fixed Point Theory and Applications 2014 (2014), Article number: 48, DOI: 10.1186/1687-1812-2014-48.

M. Jain, K. Tas, S. Kumar and N. Gupta, Coupled common fixed point results involving a (ϕ,ψ)-contractive condition for mixed g-monotone operators in partially ordered metric spaces, Journal of Inequalities and Applications 2012 (2012), Article number: 285, DOI: 10.1186/1029-242X-2012-285.

P. Kanchanapally and V. N. Raju, Common fixed point theorem in a multiplicative S-metric space with an application, Communications in Mathematics and Applications 12(2) (2021), 303 – 314, DOI: 10.26713/cma.v12i2.1495.

E. Karapınar, Couple fixed point theorems for nonlinear contractions in cone metric spaces, Computers & Mathematics with Applications 59(12) (2010), 3656 – 3668, DOI: 10.1016/j.camwa.2010.03.062.

V. Lakshmikantham and Lj. C´ iric´, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis: Theory, Methods & Applications 70(12) (2009), 4341 – 4349, DOI: 10.1016/j.na.2008.09.020.

M. Mohammad, R. Jamal, J. Mishra, Q. A. Kabir and R. Bhardwaj, Coupled fixed point theorem and dislocated quasi-metric space, International Journal of Pure and Applied Mathematics 119(10) (2018), 1249 – 1260.

S. Sedghi, N. Shobe and A. Aliouche, A generalization of fixed point theorem in S-metric spaces, Matematicki Vesnik 64(3) (2012), 258 – 266, URL: http://www.vesnik.math.rs/landing.php?p=mv123.cap&name=mv12309.

W. Shatanawi, B. Samet and M. Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Mathematical and Computer Modelling 55(3-4) (2012), 680 – 687, DOI: 10.1016/j.mcm.2011.08.042.

N. Singh, D. Singh, A. Badal and V. Joshi, Fixed point theorems in complex valued metric spaces, Journal of the Egyptian Mathematical Society 24(3) (2016), 402 – 409, DOI: 10.1016/j.joems.2015.04.005.

Downloads

Published

30-11-2024

How to Cite

Gandhi, M. P., Aserkar, A. A., & Chib, S. (2024). A Study of Coupled Fixed Point in Multiplicative S-Metric Space. Communications in Mathematics and Applications, 15(3), 1089–1098. https://doi.org/10.26713/cma.v15i3.2779

Issue

Section

Research Article