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Thermal Applications of Stability Analysis of Cubic Functional Equation in Banach Spaces and Intuitionistic Fuzzy Normed Spaces

Author

Listed:
  • Subramani Karthikeyan
  • Kandhasamy Tamilvanan
  • John Michael Rassias
  • Masho Jima Kabeto

Abstract

This paper analyzes the stability of the Euler–Lagrange–Jensen cubic functional equation in the context of Banach spaces and Intuitionistic Fuzzy Normed Spaces (IFN‐Spaces). We use both direct and fixed point techniques to establish the generalized Ulam stability of the cubic functional equation under various norm‐based constraints. The theoretical conclusions are then applied to thermal settings, with temperature distributions modeled over discrete grid points. Our investigation shows nonlinear temperature profiles can be effectively expressed by cubic functional equations, with stability maintained under the defined conditions. These findings provide important insights into the use of functional equations to solve real‐world problems involving heat dispersion and associated thermal phenomena.

Suggested Citation

  • Subramani Karthikeyan & Kandhasamy Tamilvanan & John Michael Rassias & Masho Jima Kabeto, 2025. "Thermal Applications of Stability Analysis of Cubic Functional Equation in Banach Spaces and Intuitionistic Fuzzy Normed Spaces," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:8791882
    DOI: 10.1155/jom/8791882
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    References listed on IDEAS

    as
    1. Mohiuddine, S.A., 2009. "Stability of Jensen functional equation in intuitionistic fuzzy normed space," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2989-2996.
    2. Mursaleen, M. & Danish Lohani, Q.M., 2009. "Intuitionistic fuzzy 2-normed space and some related concepts," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 224-234.
    3. Saadati, R. & Sedghi, S. & Shobe, N., 2008. "Modified intuitionistic fuzzy metric spaces and some fixed point theorems," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 36-47.
    4. Mursaleen, M. & Mohiuddine, S.A., 2009. "On stability of a cubic functional equation in intuitionistic fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2997-3005.
    5. Abdulaziz M. Alanazi & G. Muhiuddin & K. Tamilvanan & Ebtehaj N. Alenze & Abdelhalim Ebaid & K. Loganathan, 2020. "Fuzzy Stability Results of Finite Variable Additive Functional Equation: Direct and Fixed Point Methods," Mathematics, MDPI, vol. 8(7), pages 1-14, June.
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