in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.

High-level ab initio calculations have been used to construct linear free-energy relationships describing the kinetics and thermodynamics of the combination and dissociation reactions between alkyl radicals and nitroxides in terms of easily accessible parameters that quantify the electronic, steric and radical stabilization characteristics of the coreactants. For the gas-phase equilibrium const...

In this paper, we prove the generalized Hyers--Ulamstability of a quadratic and quartic functional equation inintuitionistic fuzzy Banach spaces.