jaem

TWMS Journal of Applied and Engineering Mathematics

2146-1147 2587-1013

Işık University Press

Operator Algebras and Functional Analysis Topology

Operatör Cebirleri ve Fonksiyonel Analiz Topoloji

UNIQUENESS OF CERTAIN FIXED POINT THEOREMS ON MULTIPLICATIVE METRIC SPACE WITH APPLICATION

https://orcid.org/0009-0009-4169-7725

R D

Mohanraj

SRM Institute of Science and Technology, Vadapalani campus

https://orcid.org/0000-0002-6872-5644

Rajesh

SRM Institute of Science and Technology, Vadapalani campus

04 07 2026

16 4 496 509 03 21 2025 07 30 2025

2010

TWMS Journal of Applied and Engineering Mathematics

In this paper, we establish few fixed point results in multiplicative metric space and prove the existence of fixed points along with its uniqueness, by employing contraction mappings in complete multiplicative metric space. We have provided few examples to validate our obtained results. Furthermore, we prove some theorems involving solutions of nonlinear integral equation as an application of our fixed point theorems.

Contraction mapping Complete multiplicative metric space Fixed point Weakly commuting mappings

[1] Agarwal, R. P., Karapinar, E. Samet, B., (2016), An essential remark on fixed point results on multiplicative metric spaces, Fixed Point Theory and applications, 21, pp. 1-3.

[2] Ansar, A., Idris, M. A., (2022), Some fixed point results on multiplicative metric spaces, Journal of Mathematics : Theory and Applications, 4 (1), pp. 15-20.

[3] Aminat, O. I., Hallowed Olaoluwa, O., Johnson Oladeru, O., (2022), Some fixed points of multivalued maps in multiplicative metric spaces, Heliyon, 8 (12), pp. e12453.

[4] Gupta, A., Maitra, J. K., Rai, V., (2018), Application of fixed point theorem for uniqueness and stability of solutions for a class of nonlinear integral equations, Journal of Applied Mathematics and Informatics, 36 (1-2), pp. 1-14.

[5] Bashirov, A. E., Kurpnar, E. M., Ozyapici, A., (2008), Multiplicative calculus and its applications, Journal of Mathematical Analysis and Applications, 337 (1), pp. 36-48.

[6] Gu, F., Cui, L. M., Wu, Y. H., (2013), Some fixed point theorems for new contractive type mappings, Journal of Qiqihar University, 19, pp. 85-89.

[7] Alshammari, I., Ali, S., Haque Khan, Q., Rashid, T., Ozel, C., (2023), Metrical fixed point results on b-multiplicative metric spaces employing binary relation, European Journal of Pure and Applied Mathematics, 16 (4), pp. 2405-2418.

[8] Kedim, I., Berzig, M., (2021), Fixed point theorems for maia α − ψ contractive type mappings with applications, Journal of Mathematical Analysis and Applications, 504 (1), pp. 1-12.

[9] Rus, I., Serban, M. A., (2013), Basic problems of the metric fixed point theory and the relevance of a metric fixed point theorem, Carpathian Journal of Mathematics, 29 (2), PP. 239-258.

[10] Jarvisvivin, J., Mary Priya Dharsini, A., (2024), Application of fixed point theorems to differential equation in b-multiplicative metric spaces, Indian Journal of Science and Technology, 17 (22), pp. 2352-2362.

[11] Wang C., Convergence, Stability and Data Dependence for Fixed Points of Generalized Nonexpansive Mappings with Applications, (2025), TWMS J. Pure Appl. Math. V.16, N.1, 2025, pp.137-148

12] Joselin Lavino, P., Mary Priya Dharsini, A., (2023), Some fixed point theorems of rational type contraction on b-multiplicative metric spaces, European Chemical Bulletin, 12, pp. 2262-2267.

[13] Yadav, K., Kumar, D., (2024), Multiplicative m-metric space, fixed point theorems with applications in multiplicative integrals equation and numerical results, Journal of Applied Analysis, 30 (1), pp. 173-186.

[14] Florack, L., Assen, H. V., (2011), Multiplicative calculus in biomedical image analysis, Journal of Mathematical Imaging and Vision, 42, pp. 64-75.

[15] Mercy Arokia Rani, J., Leema Maria Prakasam, A., (2024), Fixed points of operators with multiplicative closed graphs on bipolar b-multiplicative metric spaces, Advances in Fixed Point Theory, 14 (2024), pp.1-16.

[16] Grossman, M., Katz, R., (1972), Non-newtonian calculus, Pigeon Cove, Lee press, Massachusats, pp. 23-35.

[17] Abbas, M., Ali, B., Suleiman, Y. I., (2015), Common fixed points of locally contractive mappings in multiplicative metric spaces with application, International Journal of Mathematics and Mathematical Sciences, 2015 (3), pp. 1-7.

[18] Nanware, J. A., Jadhav, N. B., Dhaigude, D. B., (2020), Existence and uniqueness of solutions of nonlinear implicit fractional differential equations, Dynamics of Continuous, Discrete and Impulsive Systems. Series A : Mathematical Analysis, 27, pp. 275-282.

[19] Kayode Adewale, O., Olusola Ayodele, S., Eriwa Oyelade, B., Ehui Aribike, E., (2024), Equivalence of some results and fixed point theorems in S-multiplicative metric spaces, Fixed Point Theory and Algorithms for Sciences and Engineering, 2024 (1), pp. 1-13.

[20] Ozavsar, M., Cevikel, A. C., (2017), Fixed point of multiplicative contraction mappings on multiplicative metric spaces, Journal of Engineering Technology and Applied Sciences, 2 (2), pp. 65-79.

[21] Acar, O., (2023), Some recent and new fixed point results on orthogonal metric-like space, Constructive Mathematical Analysis, 6 (3), pp. 184-197.

[22] Shukla, S., (2016), Some critical remarks on the multiplicative metric spaces and fixed point results, Journal of Advanced Mathematical Studies, 9 (3), pp. 454-458.

[23] Shoaib, A., Saleemullah, M., (2020), Some fixed point results in b-multiplicative metric space, TWMS J. App. and Eng. Math., 10 (4), pp. 846-856.

[24] Sudheer Kumar, P., Jagannadha Rao, G. V. V., Santhi Kumar, R., Satyanarayana, P. E., (2024), Fixed point theorems for a pair of (α, η, ψ)- geraghty contraction type maps in complete metric spaces, Nonlinear Functional Analysis and Applications, 29 (1), pp. 57-67.

[25] Rasham, T., De La Sen, M., (2022), A novel study for hybrid pair of multivalued dominated mappings in b-multiplicative metric space with applications, Journal of Inequalities and Applications, 107, pp. 1-15.

[26] Dosenovic, T., Postolache, M., Radenovic, S., (2016), On multiplicative metric spaces : survey, Fixed Point Theory and Applications, 92 (2016), pp. 1-17.

[27] Dosenovic, T., Radenovic, S., (2018), Multiplicative metric spaces and contractions of rational type, Advances in the theory of Nonlinear Analysis and Applications, 2 (4), pp. 195-201.