A Result on probabilistic 2-metric space using strong semi compatible mappings

V Srinivas; K Satyanna

doi:10.17485/IJST/v14i47.1513

Article

A Result on probabilistic 2-metric space using strong semi compatible mappings

VIEWS 1229
PDF 205

Indian Journal of Science and Technology

DOI: 10.17485/IJST/v14i47.1513

Year: 2021, Volume: 14, Issue: 47, Pages: 3467-3474

Original Article

A Result on probabilistic 2-metric space using strong semi compatible mappings

V Srinivas¹, K Satyanna^2*

¹Assistant Professor, Department of Mathematics, University college of Science, Osmania University, 500004, Telangana, India
²Assistant Professor, Department of Mathematics, M.A.L.D. Government Degree College, Palamoor University, Gadwal, Mahaboobnagar, 509125, Telangana

*Correspoding Author
Email: [email protected]

Received Date:19 August 2021, Accepted Date:27 November 2021, Published Date:27 December 2021

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

Abstract

Objective/Aim: To generate a fixed point theorem in probabilistic 2-metric space. Method: By employing strong semi compatible mappings and sub sequentially continuous mappings. Findings: Generated unique common fixed point theorem and substantiated with appropriate example. Novelty/ Improvement: The concepts of strong semi compatible mappings and sub sequentially continuous mappings are weaker than existing conditions like weakly compatible mappings which generalizes the theorem of V. K. Gupta, Arihant Jain and Rajesh kumar.

Keywords: Strong semi compatible; sub sequentially continuous; Probabilistic 2metric space; conditional semi compatible; conditional compatible

References

Karl M. Statistical metrics. Proceedings of the National Academy of Sciences of the. 1942;28(12):535. Available from: https://doi.org/10.1073/pnas.28.12.535
Dhananjay G, Kumam P, Abbas M. Background and Recent Developments of Metric Fixed Point Theory. 2017.
Mishra SN. Common fixed points of compatible mappings in PM-spaces. Math. Japon. 1931;36:283–289. Available from: https://ci.nii.ac.jp/naid/10010237904/
Martinez-Moreno J, Gopal D, Perov A. Version of Fuzzy Metric Spaces and Common Fixed Points for Compatible Mappings. Mathematics . 2021;9:1290. Available from: https:// dx.doi.org/10.3390/math9111290
Bijendra S, Shishir J. Semi-compatibility and fixed point theorems in Menger Space. Journal of the Chungcheong Mathematical Society. 2004;17(1):1–7. Available from: http://www.ccms.or.kr/data/pdfpaper/jcms17 1/1711.pdf
Zhou M, Jain MK, Khan MS. Semi-compatible mappings and common fixed point theorems of an implicit relation via inverse $ C-$ class functions. AIMS Mathematics . 2021;6(3):2636–2652. Available from: . https://doi.org/10.3934/math.678.2021160
Sunny C, Suneel K, Pant BD. Common fixed point theorems for occasionally weakly compatible mappings in Menger spaces. Journal of Advanced Research in Pure Mathematics. 2021;3(4):17–23. Available from: https://doi.org/10.5373/jarpm.678.122010
Patel DK, Kumam P, Gopal D. Some discussion on the existence of common fixed points for a pair of maps. Fixed Point Theory and Applications . 2013;2013(1):1–17. Available from: https://doi.org/10.1186/1687-1812-2013-187
Mukesh KJ, Saeed KM. Generalization Of Semi Compatibility With Some Fixed Point Theorems Under Strict Contractive Condition. Applied Mathematics E-Notes. 2017;1(17):25–35. Available from: http://www.math.nthu.edu.tw/amen/
Ravindra KB, Naseer S. Faintly compatible mappings and common fixed Points. Fixed point theory and applications. 2013;2013(1):1–19. Available from: https://doi.org/10.1186/1687-1812-2013-156
Arihant J, Gupta VK, Rajesh K. Fixed Point Theorem using Absorbing Mappings in Fuzzy Metric Space. Annals of Pure and Applied Mathematics. 2019;19(2):161–167. Available from: https://doi.org/10.22457/apam.609v19n2a4
Srinivas V, Satyanna K. Some results in Menger space by using sub compatible, faintly compatible mappings. Malaya Journal of Matematik. 2021;9(1):725–730. Available from: https://dx.doi.org/10.26637/mjm0901/0127
Satyanna K, Srinvas V. Fixed point theorem using semi compatible and sub sequentially continuous mappings in Menger space. Journal of Mathematical and Computational Science . 2020;10(6):2503–2515. Available from: https://doi.org/10.28919/jmcs/4953
Srinivas V, Thirupathi T. A result on Banach space using E.A like property. Indian Journal of Science and Technology. 2020;13(44):4490–4499. Available from: https://dx.doi.org/10.17485/IJST/v13i44.1909
Sharma R, Ansari HA. Some fixed point theorems in an intuitionistic Menger space via C‐class and inverse C‐class functions. Computational and Mathematical Methods. 2020;2(4):e1090. Available from: https://doi.org/10.1002/cmm4.1090
Zidan AM. Partial Metric Spaces with some Results in Common Fixed Point Theorems. Journal of Function Spaces. 2021;2021:1–9. Available from: https://doi.org/10.1155/2021/5586936

Copyright

© 2021 Srinivas & Satyanna. 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)