Refinements of generalized Aczél–Popoviciu’s inequality and Bellman’s inequality

In this paper, using the method of Diaz-Barrero et al. (2008) [J.L. Diaz-Barrero, M. Grau-Sanchez, P.G. Popescu, Refinements of Aczél, Popoviciu and Bellman’s inequalities, Comput. Math. Appl. 56 (2008) 2356–2359], refinements of generalized Aczél-Popoviciu’s inequality and generalized Bellman’s inequalities are established. As applications, some integral inequalities are given.