Common Fixed Point Theorem in a Multiplicative <it>S</it>-Metric Space With an Application

Authors

  • Prasad Kanchanapally Department of Mathematics, University College of Science, Osmania University, Hyderabad 500007
  • V. Naga Raju Department of Mathematics, University College of Science, Osmania University, Hyderabad 500007

DOI:

https://doi.org/10.26713/cma.v12i2.1495

Keywords:

Multipicative S-metric, Common fixed point, Multiplicative S-convergent sequence, Multiplicative S-complete metric space, Multiplicative S-continuous

Abstract

In this paper, we introduce multiplicative \(S\)-metric space as a generalization of multiplicative \(d\)-metric space and investigate its some topological properties. Further, we establish a common fixed point theorem for a pair of self maps in the framework of multiplicative \(S\)-metric space with an application. This result generalizes some fixed point results in the current literature. Finally, we provide an example in support of the result.

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References

M. Abbas, M. De La Sen and T. Nazir, Common fixed points of generalized rational type cocyclic mappings in multiplicative metric spaces, Discrete Dynamic in Nature and Society 2015 (2015), Article ID 532725, DOI: 10.1155/2015/532725.

M. Abbas, B. Ali and Y.I. Suleiman, Common fixed points of locally contractive mappings in multiplicative metric spaces with application, International Journal of Mathematics and Mathematical Sciences 2015 (2015), Article ID 218683, DOI: 10.1155/2015/218683.

A.E. Bashirov, E.M. Kurplnara and A. Ozyapici, Multiplicative calculus and its applications, Journal of Mathematical Analysis and Applications 337 (2008), 36 – 48, DOI: 10.1016/j.jmaa.2007.03.081.

S. Czerwik, Contraction mappings in b-metric spaces, Communications in Mathematics 1 (1993), 5 – 11, http://dml.cz/dmlcz/120469.

L. Florack and H.V. Assen, Multiplicative calculus in biomedical image analysis, Journal of Mathematical Imaging and Vision 42(1) (2012), 64 – 75, DOI: 10.1007/s10851-011-0275-1.

M. Grossman and R. Katz, Non-Newtonian Calculus, Pigeon Cove, Lee Press, Massachusats (1972).

S.M. Kang, P. Kumar, S. Kumar, P. Nagpal and S.K. Garg, Common fixed points for compatible mappings and its variants in multiplicative metric spaces, International Journal of Pure and Applied Mathematics 42(1) 102(2), (2015), 383 – 406, DOI: 10.12732/ijpam.v102i2.14.

C. Mongkolkeha andW. Sintunavarat, Best proximity points for multiplicative proximal contraction mapping on multiplicative metric spaces, Journal of Nonlinear Sciences and Applications 8 (2015), 1134 – 1140, DOI: 10.22436/jnsa.008.06.22.

H. Nakano, Modular Semi-Ordered Linear Spaces, Maruzen, Tokyo (1950).

M. Ozavsar and A.C. Cevikel, Fixed point of multiplicative contraction mappings on multiplicative metric spaces, (2012), URL:https://arxiv.org/abs/1205.5131.

N.Y. Ozgur and N. Tas, Some generalizations of fixed point theorems on S-metric spaces, in Essays in Mathematics and Its Applications, in Honor of Vladimir Arnold, pp. 229 – 261, New York, Springer (2016), DOI: 10.1007/978-3-319-31338-2_11.

S. Sedghi, N. Shobe and H. Zhou, A common fixed point theorem in D¤-metric space, Fixed Point Theory and Applications 2007 (2007), Article number: 027906, DOI: 10.1155/2007/27906.

S. Sedghi, N. Shobe and A. Aliouche, A generalization of fixed point theorem in S-metric spaces, Matematiˇcki Vesnik 64 (2012), 258 – 266, https://emis.de/journals/MV/123/mv12309.pdf.

S. Sedghi, A. Gholidahneh, T. Dosenovi´c, J. Esfahani and S. Radenovi, Common fixed point of four maps in Sb-metric spaces, Journal of Linear and Topological Algebra 5(2) (2016), 93 – 104, http://jlta.iauctb.ac.ir/article_523028_f5e63d18f0cde338db78527fb4edf152.pdf.

W.A. Wilson, On quasi-metric spaces, American Journal of Mathematics 53(3) (1931), 675 – 684, DOI: 10.2307/2371174.

O. Yamaod and W. Sintunavarat, Some fixed point results for generalized contraction mappings with cyclic (®,¯)-admissible mappings in multiplicative metric space, Journal of Inequalities and Applications 2014 (2014), Article number: 488, DOI: 10.1186/1029-242X-2014-488.

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Published

30-06-2021
CITATION

How to Cite

Kanchanapally, P., & Raju, V. N. (2021). Common Fixed Point Theorem in a Multiplicative <it>S</it>-Metric Space With an Application. Communications in Mathematics and Applications, 12(2), 303–314. https://doi.org/10.26713/cma.v12i2.1495

Issue

Vol. 12 No. 2 (2021)

Section

Research Article

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