A Fixed Point Result with (CLR) Property in S-Metric Spaces

V Sambasiva Rao; Uma Dixit

doi:10.17485/IJST/v15i37.1053

Article

A Fixed Point Result with (CLR) Property in S-Metric Spaces

VIEWS 1197
PDF 277

Indian Journal of Science and Technology

DOI: 10.17485/IJST/v15i37.1053

Year: 2022, Volume: 15, Issue: 37, Pages: 1842-1849

Original Article

A Fixed Point Result with (CLR) Property in S-Metric Spaces

V Sambasiva Rao^1*, Uma Dixit²

¹Department of Mathematics, Osmania University, Hyderabad, 500007, Telangana, India
²Department of Mathematics, University Post Graduate College, Osmania University,
Secunderabad, 500003, Telangana, India

*Corresponding Author
Email: [email protected]

Received Date:16 May 2022, Accepted Date:14 July 2022, Published Date:26 September 2022

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objective : The present paper is an attempt to improve results on fixed point theorems for four pairwise occasionally weakly compatible (owc) mappings in S-metric spaces. Method: We have applied quadratic inequality to prove certain fixed-point results for four pairwise owc mappings under weaker conditions using (CLR) property. Findings: We have generalized and expanded some already existing results in the literature and new results are obtained that generated the common fixed points in S-metric spaces. Befitting examples are given to support our findings. Novelty: Existence and uniqueness of fixed points in S-metric spaces are established by using (CLRFG) property even in the absence of containment conditions. 2010 Mathematics Subject Classification: 47H10, 54H25

Keywords: Smetric Space; Coincidence Point; Common Fixed Point; Occasional Weak Compatibility; (CLR) Property

References

Jungck G. Commuting Mappings and Fixed Points. The American Mathematical Monthly. 1976;83(4):261–263. Available from: https://doi.org/10.1080/00029890.1976.11994093
Jungck G. Compatible mappings and common fixed points. International Journal of Mathematics and Mathematical Sciences. 1986;9(4):771–779. Available from: https://doi.org/10.1155/S0161171286000935
Jungck G, Rhoades BE. Fixed points for set valued functions without continuity. Indian Journal of pure and applied mathematics. 1998;29:227–238. Available from: https://www.researchgate.net/publication/236801026_Fixed_Points_for_Set_Valued_Functions_Without_Continuity
Al-Thagafi MA, Shahzad N. Generalized I-nonexpansive selfmaps and invariant approximations. Acta Mathematica Sinica, English Series. 2008;24(5):867–876. Available from: https://doi.org/10.1007/s10114-007-5598-x
Aamri M, Moutawakil DE. Some new common fixed point theorems under strict contractive conditions. Journal of Mathematical Analysis and Applications. 2002;270:59–67. Available from: https://doi.org/10.1016/S0022-247X(02)00059-8
Sintunavarat W, Kumam P. Common Fixed Point Theorems for a Pair of Weakly Compatible Mappings in Fuzzy Metric Spaces. Journal of Applied Mathematics. 2011;2011:1–14. Available from: https://doi.org/10.1155/2011/637958
Limprayoon J, Kitkuan D. The (CLR)-property and common fixed point theorems in b-metric spaces. Advances in Mathematics: Scientific Journal. 2021;10(6):2821–2829. Available from: https://www.research-publication.com/amsj/uploads/papers/vol-10/iss-06/AMSJ-2021-N06-10.pdf
Nikbakhtsarvestani F, Vaezpour SM, Asadi M. Common Fixed Point Theorems for Weakly Compatible Mappings by (CLR) Property on Partial Metric Space. Iranian Journal of Mathematical Sciences and Informatics. 2019;14:19–32. Available from: https://doi.org/10.7508/ijmsi.2019.02.003
Gnanaprakasam, Joseph A. Existence and Uniqueness of Common Fixed Point on Complex Partial-Metric Space. Journal of Function Spaces. 2022;p. 2022. Available from: https://doi.org/10.1155/2022/1925612
Srinivas V, Satyanna K. Some Results by Using CLR’s-Property in Probabilistic 2-Metric Space. International Journal of Analysis and Applications. 2021;19(6):904–914. Available from: https://doi.org/10.28924/2291-8639-19-2021-904
Kanchanapally P, V. NR. Common fixed points in S-metric spaces using EA and CLR-properties. Malaya Journal of Matematik. 2020;8(3):1273–1277. Available from: https://doi.org/10.26637/MJM0803/0095
Gupta V, Shatanawi W, Kanwar A. Coupled Fixed Point Theorems Employing CLR-Property on V -Fuzzy Metric Spaces. Mathematics. 2020;8(3):404. Available from: https://doi.org/10.3390/math8030404
Sedghi S, Shobe N, Aliouche A. A generalization of fixed point theorems in $ S $-metric spaces. 2012;249:258–266. Available from: https://eudml.org/serve/253803/accessibleLayeredPdf/0
Mustafa Z, Sims B. A new approach to generalized metric spaces. Journal of Nonlinear and convex Analysis. 2006;7(2):289.
Sedghi S, Shobe N, Zhou H. A Common Fixed Point Theorem in -Metric Spaces. Fixed Point Theory and Applications. 2007;2007(1):027906. Available from: https://doi.org/10.1155/2007/27906
Mlaiki N, Özgür NY, Taş N. New Fixed-Point Theorems on an S-metric Space via Simulation Functions. Mathematics. 2019;7(7):583. Available from: https://doi.org/10.3390/math7070583
Saluja GS, Kim WHJK, Lim. Common fixed point theorems under generalized (ψ-ϕ)-weak contractions in S-metric spaces with applications. Nonlinear Functional Analysis and Applications. 2021;26:13–33. Available from: https://doi.org/10.22771/nfaa.2021.26.01.02
Sedghi S, Dung NV. Fixed point theorems in fuzzy metric spaces. 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS). 2013;255:113–124. Available from: https://eudml.org/serve/261245/accessibleLayeredPdf/0
Chauhan S. Fixed points of weakly compatible mappings in fuzzy metric spaces satisfying common limit in the range property. Indian J. Math. 2012;54:375–397.
Taş K, Telci M, Fisher B. Common fixed point theorems for compatible mappings. International Journal of Mathematics and Mathematical Sciences. 1996;19(3):451–456. Available from: https://doi.org/10.1155/S0161171296000646
Babu GVR, Kameswari MVR. Common fixed point theorems for weakly compatible maps using a contraction quadratic inequality, Adv. Stud. Contemp. Math. 2004;9:139–152. Available from: https://www.researchgate.net/publication/268887489_Common_fixed_point_theorems_for_weakly_compatible_maps_using_a_contraction_quadratic_inequality
Babu GVR, Alemayehu GN. Common fixed point theorems for occasionally weakly compatible maps satisfying property (E. A) using an inequality involving quadratic terms. Applied Mathematics Letters. 2011;24(6):975–981. Available from: https://doi.org/10.1016/j.aml.2011.01.008

Copyright

© 2022 Rao & Dixit. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Published By Indian Society for Education and Environment (iSee)