General Quadratic-Additive Type Functional Equation and Its Stability

Abstract EN

We investigate the general functional equation of the form f ( a x + b y + c z ) - a b f ( x + y ) - b c f ( y + z ) − a c f ( x + z ) - a ( ( a + 1 ) / 2 - b - c ) f ( x ) - b ( ( b + 1 ) / 2 - a - c ) f ( y ) - c ( ( c + 1 ) / 2 - a - b ) f ( z ) - ( a ( a - 1 ) / 2 ) f ( - x ) − ( b ( b - 1 ) / 2 ) f ( - y ) - ( c ( c - 1 ) / 2 ) f ( - z ) = 0 , whose solutions are quadratic-additive mappings in connection with stability problems.