Exploring Profit Opportunities in Intuitionistic Fuzzy Metric Spaces via Edelstein Type Mappings

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-22-2024-143
Published: Aug 20, 2024
Cite as:
J. Johnsy, M. Jeyaraman, Rahul Shukla, R. Venkatesan, Exploring Profit Opportunities in Intuitionistic Fuzzy Metric Spaces via Edelstein Type Mappings, Int. J. Anal. Appl., 22 (2024), 143.

Main Article Content

J. Johnsy, M. Jeyaraman, Rahul Shukla, R. Venkatesan

Abstract

This paper establishes a break-even point theorem concerning a set of mappings adhering to an Edelstein-type contractive criterian within intuitionistic fuzzy metric domains. It explores the break-even analysis within a straightforward total cost-revenue model applicable to dynamic businesses. Utilizing the coincident point theorem within intuitionistic fuzzy metric space, the study demonstrates the inclination of profit-sensitive (or loss-sensitive) dynamic businesses towards their respective break-even points.

Article Details

References

  1. K.T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets Syst. 20 (1986), 87–96. https://doi.org/10.1016/s0165-0114(86)80034-3.
  2. M. Abbas, N. Saleem, M. De la Sen, Optimal Coincidence Point Results in Partially Ordered Non-Archimedean Fuzzy Metric Spaces, Fixed Point Theory Appl. 2016 (2016), 44. https://doi.org/10.1186/s13663-016-0534-3.
  3. S. Banach, Sur les Opérations dans les Ensembles Abstraits et leur Application aux Équations Intégrales, Fund. Math. 3 (1922), 133–181. https://doi.org/10.4064/fm-3-1-133-181.
  4. M. Dolmatova, A. Vasin, H. Gao, Supply Function Auction for Linear Asymmetric Oligopoly: Equilibrium and Convergence, Procedia Computer Sci. 55 (2015), 112–118. https://doi.org/10.1016/j.procs.2015.07.015.
  5. M. Edelstein, On Fixed and Periodic Points Under Contractive Mappings, J. London Math. Soc. s1-37 (1962), 74–79. https://doi.org/10.1112/jlms/s1-37.1.74.
  6. A. George, P. Veeramani, On Some Results in Fuzzy Metric Spaces, Fuzzy Sets Syst. 64 (1994), 395–399. https://doi.org/10.1016/0165-0114(94)90162-7.
  7. A. Hussain, U. Ishtiaq, K. Ahmed, H. Al-Sulami, On Pentagonal Controlled Fuzzy Metric Spaces with an Application to Dynamic Market Equilibrium, J. Function Spaces. 2022 (2022), 5301293. https://doi.org/10.1155/2022/5301293.
  8. M. Jeyaraman, D. Poovaragavan, Fixed Point Theorems in Generalized Intuitionistic Fuzzy Metric Spaces Using Contractive Condition of Integral Type, Malaya J. Mat. S (2019), 126–129. https://doi.org/10.26637/mjm0s01/0030.
  9. M. Jeyaraman, Some Common Fixed Point Theorems for (Phi, Psi)-Weak Contractions in Intuitionistic Generalized Fuzzy Cone Metric Spaces, Malaya J. Mat. S (2019), 154–159. https://doi.org/10.26637/mjm0s01/0036.
  10. G. Jungck, S. Radenovic, S. Radojevic, V. Rakocevic, Common Fixed Point Theorems for Weakly Compatible Pairs on Cone Metric Spaces, Fixed Point Theory Appl. 2009 (2009), 643840. https://doi.org/10.1155/2009/643840.
  11. G. Jungck, Periodic and Fixed Points, and Commuting Mappings, Proc. Amer. Math. Soc. 76 (1979), 333–338.
  12. I. Kramosil, J. Michálek, Fuzzy Metrics and Statistical Metric Spaces, Kybernetika, 11 (1975), 336–344. http://dml.cz/dmlcz/125556.
  13. I. Mezník, Banach Fixed Point Theorem and the Stability of the Market, in: Proceedings of the International Conference on Mathematics Education into the 21st Century Project, The Decidable and the Undecidable in Mathematics Education, Brno, Czech Republic, 2003.
  14. D. Mihe¸t, On Fuzzy Contractive Mappings in Fuzzy Metric Spaces, Fuzzy Sets Syst. 158 (2007), 915–921. https://doi.org/10.1016/j.fss.2006.11.012.
  15. Z. Mustafa, V. Parvaneh, M. Abbas, J.R. Roshan, Some Coincidence Point Results for Generalized (ψ, φ)-Weakly Contractive Mapping in Ordered G-Metric Spaces, Fixed Point Theory Appl. 2013 (2013), 326. https://doi.org/10.1186/1687-1812-2013-326.
  16. J.H. Park, Intuitionistic Fuzzy Metric Spaces, Chaos Solitons Fractals. 22 (2004), 1039–1046. https://doi.org/10.1016/j.chaos.2004.02.051.
  17. S. Shukla, D. Gopal, W. Sintunavarat, A New Class of Fuzzy Contractive Mappings and Fixed Point Theorems, Fuzzy Sets Syst. 350 (2018), 85–94. https://doi.org/10.1016/j.fss.2018.02.010.
  18. S. Shukla, N. Dubey, R. Shukla, I. Mezník, Coincidence Point of Edelstein Type Mappings in Fuzzy Metric Spaces and Application to the Stability of Dynamic Markets, Axioms. 12 (2023), 854. https://doi.org/10.3390/axioms12090854.
  19. Naveen Mani, Megha Pingale, Rahul Shukla, Renu Pathak, Fixed point theorems in fuzzy b-metric spaces using two different t-norms, Adv. Fixed Point Theory, 13 (2023), 29. https://doi.org/10.28919/afpt/8235.
  20. V. Gupta, G. Jungck, N. Mani, Common Fixed Point Theorems for New Contraction Without Continuity Completeness and Compatibility Property in Partially Ordered Fuzzy Metric Spaces, Proc. Jangjeon Math. Soc. 22 (2019), 51–57.
  21. V. Gupta, R.K. Saini, N. Mani, A.K. Tripathi, Fixed Point Theorems Using Control Function in Fuzzy Metric Spaces, Cogent Math. 2 (2015), 1053173. https://doi.org/10.1080/23311835.2015.1053173.
  22. V. Gupta, N. Mani, R. Sharma, A.K. Tripathi, Some Fixed Point Results and Their Applications on Integral Type Contractive Condition in Fuzzy Metric Spaces, Bol. Soc. Paran. Mat. 40 (2022), 1–9. https://doi.org/10.5269/bspm.51777.
  23. L.A. Zadeh, Fuzzy Sets, Inf. Control. 8 (1965), 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x.