Fixed points and quadratic rho-functional equations

Quadratic $alpha$-functional equations

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.

Quadratic $rho$-functional inequalities in $beta$-homogeneous normed spaces

In cite{p}, Park introduced the quadratic $rho$-functional inequalitiesbegin{eqnarray}label{E01}&& |f(x+y)+f(x-y)-2f(x)-2f(y)| \ && qquad le  left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) -  f(y)right)right|,  nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|

Fixed Points and Generalized Hyers–ulam Stability of Quadratic Functional Equations

Let X, Y be complex vector spaces. It is shown that if a mapping f : X → Y satisfies f (x + iy) + f (x− iy) = 2f (x) − 2f (y) (0.1) or f (x + iy) − f (ix + y) = 2f (x) − 2f (y) (0.2) for all x, y ∈ X , then the mapping f : X → Y satisfies f (x + y) + f (x− y) = 2f (x) + 2f (y) for all x, y ∈ X . Furthermore, we prove the generalized Hyers-Ulam stability of the functional equations (0.1) and (0....

Fixed Points and Stability of a Generalized Quadratic Functional Equation

A fixed point approach to the stability of additive-quadratic-quartic functional equations

In this article, we introduce a class of the generalized mixed additive, quadratic and quartic functional equations and obtain their common solutions. We also investigate the stability of such modified functional equations in the non-Archimedean normed spaces by a fixed point method.