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.

A bstract We investigate the phase shifts of low-energy ? - scattering under variations fundamental parameters Standard Model, namely light quark mass, electromagnetic fine-structure constant as well QCD ? -angle. As a first step, we recalculate in our Universe utilizing various improvements adiabatic projection method, which leads to an improved, parameter-free prediction S- and D-wave for lab...