Quadratic functional equations of Pexider type

Quadratic Functional Equations of Pexider Type

First, the quadratic functional equation of Pexider type will be solved. By applying this result, we will also solve some functional equations of Pexider type which are closely associated with the quadratic equation.

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.

Superstability of Some Pexider-Type Functional Equation

Pexider Functional Equations Their Fuzzy Analogs 529

may be interpreted as giving the amount of information I due to two independent events A and B with probabilities p and q, respectively. The functional equation (1.1) is one of Cauchy equations, and has been dealt with extensively (see Aczdl [1-2]). However, it is more often than not that we do not have the exact values of the probabilities p and q because not enough data is available or becaus...

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.