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

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.