On the Stability of the Functional Equation
f(2x+y)+f(x+y2)=2f(x)f(y)f(x)+f(y)+2f(x+y)f(y-x)3f(y-x)-f(x+y)f\left( {2x + y} \right) + f\left( {{{x + y} \over 2}} \right) = {{2f\left( x \right)f\left( y \right)} \over {f\left( x \right) + f\left( y \right)}} + {{2f\left( {x + y} \right)f\left( {y - x} \right)} \over {3f\left( {y - x} \right) - f\left( {x + y} \right)}}

Idir, Sadani

doi:10.2478/tmmp-2020-0019

Abstract

The aim of this paper is to obtain the general solution to a reciprocal functional equation of the form $f (2 x + y) + f (\frac{x + y}{2}) = \frac{2 f (x) f (y)}{f (x) + f (y)} + \frac{2 f (x + y) f (y - x)}{3 f (y - x) - f (x + y)}$ f\left( {2x + y} \right) + f\left( {{{x + y} \over 2}} \right) = {{2f\left( x \right)f\left( y \right)} \over {f\left( x \right) + f\left( y \right)}} + {{2f\left( {x + y} \right)f\left( {y - x} \right)} \over {3f\left( {y - x} \right) - f\left( {x + y} \right)}} and to investigate its generalized Hyers-Ulam-Rassias stability.

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