A Fixed Point theorem on S_b-metric spaces with a weak S_b-metric

K.P.R. Sastry¹ , K.K.M. Sarma² , P. Krishna Kumari³

Section:Research Paper, Product Type: Journal-Paper
Vol.6 , Issue.5 , pp.7-11, Oct-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i5.711

Online published on Oct 31, 2019

Copyright © K.P.R. Sastry, K.K.M. Sarma, P. Krishna Kumari . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

384 Views    366 Downloads    135 Downloads

Abstract :
In this paper we define weak S_b-metric on a S_b-metric space which is an extension of weak S-metric on a S-metric space. We establish a fixed point theorem on S_b-metric space with a weak S_b-metric. Examples are given at relevant places. We obtain the result of K.Sarada., V.Jhansi Rani., V.Siva Rama Prasad., as a corollary. We also obtain Banach Contraction principle as a corollary

Key-Words / Index Term :
S-metric space and weak S-metric, S_b-metric space, weak S_b-metric, fixed point

References :
[1] S. Sedghi, N. Shobe, A. Aliouche, “A generalization of fixed point theorem in S-metric spaces”, Mat. Vesnik, 64, No. 3, pp.258-266, 2012.
[2] A.H. Ansari, N. Jamnian, “Best proximity point for proximal contractive type mappings with C-class functions in S-metric spaces”, Fixed Point theory and applications.– 2017:12-DOI/o – 1186/S13663 – 017- 0606-2, 2017.
[3] N.T. Hieu, N.T. Thanhly, N.V. Dury, “A generalization of ciric quasi contraction for mapping on S-metric spaces”, Thai.J. .Math – 13 (2), pp.369-380, 2014.
[4] K. Prudhvi, “Some fixed point results in S-metric spaces”, Journal of Mathematical Sciences and Applications. Vol.-4-No. 1, pp.1-3, doi: 10.12691/Jmsa- 4-1-1- Research Article, 2016.
[5] K.P.R. Sastry, K.K.M. Sarma, P. Krishna Kumari, Sunitha Choudari, “Fixed point theorems for ψ–contractions in S-metric spaces and KKS metric spaces”, International Journal of Mathematics and its applications, Volume 5, Issue 4- E, pp.619-632 with ISSN: 2347- 1557, 2017.
[6] S. Sedghi, I. Altun, N. Shobe, M. Salahshour, “Some properties of S-metric spaces and fixed point results”, Kyung pook Mathematical Journal.54 (1), pp.113- 122, 2014.
[7] S. Sedghi, N. Shobe, T. Dosenovic, “Fixed point results in S-metric spaces”, Non-linear function Anal. Appl. 20 (1), pp.55-67, 2015.
[8] S. Sedghi, A. Gholidahnh, T. Dosenovic, J. Esfahani, S. Randenovic, “Common fixed point of four maps in S_b-metric spaces”, J. Linear Topol. Algebra 5(2), pp.93-104, 2016.
[9] Nizar Souayah, Nabil Mlaiki, “A fixed point theorem in S_b-metric spaces”, Journal of Mathematics and Computer Science, 16, pp.131- 139, 2016.
[10] N. Saleem, A.H. Ansari, Parvovico, S. Radenovic, “Some new results in the framework of S_b-metric spaces”, Scientific Publications of the state university of Novi Pazar. SER. A: APPL. MATH. INFORM. AND. MECH. Vol.9. 2, pp.151-165, 2017.
[11] K.P.R. Sastry, K.K.M. Sarma, P. Krishna Kumari, “Fixed point theorems for (ψ-φ-λ) contractions in S_b- metric spaces”, International Journal of Mathematics Trends and Technology (IJMTT) Volume 66, pp.1-12 with ISSN: 2349-5758, April 2018.
[12] K. Sarada., V. Jhansi Rani., V. Siva Rama Prasad, “A fixed point theorem on S-metric space with a weak S-metric”, International Journal of Mathematical Archive-7 (1), pp.188-191, ISSN 2229-5046, 2016.