Similar to his papers [Adv. Difference Equ. 2007, Article ID 90405 (2007; Zbl 1148.39024)] and [Banach J. Math. Anal. 1, No. 2, 227–236, electronic only (2007; Zbl 1129.39013)], the author investigates the superstability of the pexiderized trigonometric functional inequality
and also stability of the Jensen type functional inequality
for each , where is an abelian group and the mappings are unknown and and are known. He also extends his results to the Banach algebras.