Fixed Point Theorems by Using Altering Distance Function in S-Metric Spaces

Authors

DOI:

https://doi.org/10.26713/cma.v13i2.1787

Keywords:

Fixed point, S-metric space, Contractive mappings, Altering distance function

Abstract

In the present paper, we prove some fixed point theorems by using the non-decreasing mapping \(\kappa :\mathbb{R}^+\to \mathbb{R}^+\) known as altering distance function or control function, in the context of \(S\)-metric space. Further, we explore the property \(P\) for these contractive mappings.

Downloads

Download data is not yet available.

References

M. Abbas and M.A. Khan, Common fixed point theorem for two mappings satisfying a generalized weak contractive condition, International Journal of Mathematics and Mathematical Sciences 2009 (2009), Article ID 131068, 9 pages, DOI: 10.1155/2009/131068.

R.P. Agarwal, M. Meehan and D. O’Regan, Fixed Point Theory and Applications, Cambridge University Press, Cambridge (2004), URL: https://books.google.co.in/books?hl=en&lr=&id=iNccsDsdbIcC&oi=fnd&pg=PP1&dq=R.P.+Agarwal,+M.+Meehan,+D.+O%E2%80%99Regan,+Fixed+Point+Theory+and+Applications.+Cambridge+University+Press.

S. Banach, Sur les opérations dans les ensembles abstraits el leur application aux équations intégrals, Fundamenta Mathematicae 3 (1992), 133 – 181, URL: http://matwbn.icm.edu.pl/ksiazki/fm/fm3/fm3120.pdf.

B.K. Das and S. Gupta, An extension of Banach contractive principle through rational expression, Indian Journal of Pure and Applied Mathematics 6 (1975), 1455 – 1458.

B.C. Dhage, A Study of Some Fixed Point Theorems, Ph.D thesis, Marathwada, Aurangabad, India (1984), URL: ??Missing.

T. Došenovic, D. Radenovic, A. Rezvani and S. Sedghi, Coincidence point theorems in S-metric spaces using integral type of contraction, UPB Scientific Bulletin, Series A: Applied Mathematics and Physics 79(4) (2017), 145 – 158, URL: https://open.uns.ac.rs/handle/123456789/3708.

N.V. Dung, N.Y. Hieu and S. Radojevic, Fixed point theorems for g-monotone maps on partially ordered S-metric spaces, Filomat 28(9) (2014), 1885 – 1898, URL: https://www.jstor.org/stable/24897683.

S. Gähler, 2-metrische Räume und ihre topologische Struktur, Mathematische Nachrichten 26(1-4) (1963/1964), 115 – 148, DOI: 10.1002/mana.19630260109.

V.R.B. Guttia and L.B. Kumssa, Fixed points of (α,ψ,ϕ)-generalized weakly contractive maps and property (P) in S-metric spaces, Filomat 31(14) (2017), 4469 – 4481, DOI: 10.2298/FIL1714469B.

G.S. Jeong and B.E. Rhoades, More maps for which F(t) = F(Tn), Demonstratio Mathematica 40 (2007), 671 – 680, DOI: 10.1515/dema-2007-0317.

A. Karami, S. Sedghi and Z.D. Mitrovic, Some coupled fixed point results for rational type contraction mappings in S-metric spaces, Malaya Journal of Mathematik 8(4) (2020), 2012 – 2020, DOI: 10.26637/MJM0804/0117.

M.S. Khan, M. Swaleh and S. Sessa, Fixed point theorems by altering distances between the points, Bulletin of the Australian Mathematical Society 30(1) (1984), 1 – 9, DOI: 10.1017/S0004972700001659.

H.G.S. Kumar, R. Bhardwaj and B.K. Singh, Fixed point theorems of soft metric space using altering distance function, International Journal of Recent Technology and Engineering 7(6) (2019), 2277 – 3878, URL: https://www.ijrte.org/wp-content/uploads/papers/v7i6/F3150037619.pdf.

Z. Mustafa and B. Sims, A new approach to generalized metric spaces, Journal of Nonlinear and Convex Analysis 7(2) (2006), 289 – 297, URL: http://yokohamapublishers.jp/online2/opjnca/vol7/p289.html.

K.H. Nashine and I. Altun, Fixed point theorems for a pair of mappings satisfying a generalized weakly contractive condition in ordered metric spaces, Hacettepe Journal of Mathematics and Statistics 41(2) (2012), 243 – 253, URL: http://www.hjms.hacettepe.edu.tr/uploads/3e9455a2-d767-444b-98bf-7ceae8cd849a.pdf.

V. Popa and M. Mocanu, Altering distance and common fixed points under implicit relations, Hacettepe Journal of Mathematics and Statistics 39(3) (2009), 329 – 357, URL: http://www.hjms.hacettepe.edu.tr/uploads/e9c462ba-d6cc-4d2a-abba-c4ddb7e9b3c7.pdf.

E. Rakotch, A note on contractive mappings, Proceedings of the American Mathematical Society 13 (1962), 459 – 465, DOI: 10.1090/S0002-9939-1962-0148046-1.

S. Sedghi and N.V. Dung, Fixed point theorems on S-metric spaces, Matematicki Vesnik 66(1) (2014), 113 – 124, URL: https://www.emis.de/journals/MV/141/mv14112.pdf.

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: https://www.emis.de/journals/MV/123/mv12309.pdf.

Downloads

Published

17-08-2022
CITATION

How to Cite

Kumar, M., Devi, S., & Singh, P. (2022). Fixed Point Theorems by Using Altering Distance Function in S-Metric Spaces. Communications in Mathematics and Applications, 13(2), 553–573. https://doi.org/10.26713/cma.v13i2.1787

Issue

Vol. 13 No. 2 (2022)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.