Refinements of generalized Aczél Popoviciuʹs inequality and Bellmanʹs 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 Bellmanʹs inequalities, Comput. Math. Appl. 56 (2008) 2356 2359], refinements of generalized Aczél-Popoviciuʹs inequality and generalized Bellmanʹs inequalities are established. As applications, some integral inequalities are given.