The stability of quadratic-reciprocal functional equation.

A new quadratic-reciprocal functional equation f ( ( k + 1 ) x + k y ) + f ( ( k + 1 ) x − k y ) = 2 f ( x ) f ( y ) [ ( k + 1 ) 2 f ( y ) + k 2 f ( x ) ] [ ( k + 1 ) 2 f ( y ) − k 2 f ( x ) ] 2 is introduced. The Hyers-Ulam stability for the quadratic-reciprocal functional equations is proved in Banach spaces using the direct method and the fixed point method, respectively. [ABSTRACT FROM AUTHOR]