A Focus on Types of Compatible Mappings in \(S\)-metric Space

Bonuga Vijayabaskerreddy; Ramachandruni Umamaheshwar Rao

doi:10.26713/cma.v13i3.1821

Authors

Bonuga Vijayabaskerreddy Division of Mathematics, Department of Science and Humanities, Sreenidhi Institute of Science and Technology (SNIST), Ghatkesar 501301, Telangana, India https://orcid.org/0000-0001-6254-3973 (unauthenticated)
Ramachandruni Umamaheshwar Rao Division of Mathematics, Department of Science and Humanities, Sreenidhi Institute of Science and Technology (SNIST), Ghatkesar 501301, Telangana, India https://orcid.org/0000-0002-6626-168X (unauthenticated)

DOI:

https://doi.org/10.26713/cma.v13i3.1821

Keywords:

S-metric space, Compatible mappings of type (A), type (B) and type (C)

Abstract

In this article, we study unique common fixed point theorems for four self mappings in S-metric space using generalized concepts of compatible mappings such as compatible mappings of type (A), type (B) and type (C). Our results are generalizing the theorems proved by Sedghi et al. (Common fixed point of four maps in S-metric spaces, Mathematical Sciences 12 (2018), 137 – 143) in metric space.

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References

G. Jungck, P. P. Murthy and Y. J. Cho, Compatible mappings of type (A) and common fixed points, Mathematica Japonica 38(1993), 381 – 390.

H. K. Pathak and M. S. Khan, Compatible mappings of type (B) and common fixed point theorems of Greguš type, Czechoslovak Mathematical Journal 45(1995), 685 – 698, DOI: 10.21136/CMJ.1995.128555.

H. K. Pathak, Y. J. Cho, S. M. Khan and B. Madharia, Compatible mappings of type (C) and common fixed point theorems of Gregus type, Demonstratio Mathematica 31(1998), 499 – 518.

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

S. Sedghi, N. Shobe and H. Zhou, A common fixed point theorem in D∗-metric spaces, Fixed Point Theory and Applications 2007(2007), Article ID 27906, 13 pages, DOI: 10.1155/2007/27906.

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

S. Sedghi, I. Altun, N. Shobe and M. A. Salahshour, Some properties of S-metric spaces and fixed point results, Kyungpook Mathematical Journal 54(1) (2014), 113 – 122, DOI: 10.5666/KMJ.2014.54.1.113.

K. Prudhvi, Fixed point theorems in S-metric spaces, Universal Journal of Computational Mathematics 3(2015), 19 – 21, DOI: 10.13189/ujcmj.2015.030201.

S. Sedghi, N. Shobkolaei, M. Shahraki and T. Došenovic, Common fixed point of four maps in S-metric spaces, Mathematical Sciences 12 (2018), 137 – 143, DOI: 10.1007/s40096-018-0252-6.

J. K. Kim, S. Sedghi, A. Gholidahneh and M. M. Rezaee, Fixed point theorems in S-metric metric spaces, East Asian Mathematical Journal 32(5) (2016), 677 – 684, DOI: 10.7858/eamj.2016.047.