Hyers Type Stability of a Radical Reciprocal Quadratic Functional Equation Originating From 3 Dimensional Pythagorean Means

Abstract

In this paper, authors introduce a 3 dimensional Pythagorean mean functional equation $$ f\left(\sqrt{x^2+y^2}\right)+f\left(\sqrt{y^2+z^2}\right)+f\left(\sqrt{z^2+x^2}\right)$$ $$=\frac{f(x)f(y)}{f(x)+f(y)}+\frac{f(y)f(z)}{f(y)+f(z)}+\frac{f(z)f(x)}{f(z)+f(x)} $$ which relates the three classical Pythagorean mean and investigate its generalized Hyers-Ulam stability.