STABILITY OF LIE BRACKET OF TRIPLE JORDAN DERIVATIONS ON TRIPLE BANACH ALGEBRA

This paper presents the mixed additive-Jensen equations and shows that a solution of it is a complex linear mapping. We also define the Lie bracket of triple Jordan derivations related to this equation in triple Banach algebra and investigate their properties. Lastly, we show the Hyers-Ulam (HU) stability of the mixed additive-Jensen equations and the Lie bracket of triple Jordan derivations on triple Banach algebra through the fixed point method, with control functions introduced by G˘avrut¸a and Rassias.