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Refinements of generalized Aczél-Popoviciu’s inequality and Bellman’s inequality. (English) Zbl 1197.26044
Summary: By using the method of {\it J.L. Diaz-Barrero, M. Grau-Sanchez} and {\it P.G. Popescu} [Comput. Math. Appl. 56, No. 9, 2356--2359 (2008; Zbl 1165.26324)], refinements of generalized Aczél-Popoviciu’s inequality and generalized Bellman’s inequalities are established. As applications, some integral inequalities are given.

26D15Inequalities for sums, series and integrals of real functions
Full Text: DOI
[1] Aczél, J.: Some general methods in the theory of functional equations in one variable, Uspekhi mat. Nauk (NS) 11, No. 3(69), 3-68 (1956) · Zbl 0070.34903
[2] Mitirinovic, D. S.; Pecaric, J. E.; Fink, A. M.: Classical and new inequalities in analysis, (1993) · Zbl 0771.26009
[3] Popoviciu, T.: On an inequality, Gaz. mat. Fiz. ser. A 11, No. 64, 451-461 (1959)
[4] Wu, S.; Debnath, L.: Generalizations of aczel’s inequality and popoviciu’s inequality, Indian J. Pure appl. Math. 36, No. 2, 49-62 (2005) · Zbl 1083.26019
[5] Wu, S.: A further generalization of aczel’s inequality and popoviciu’s inequality, Math. inequal. Appl. 10, No. 3, 565-573 (2007) · Zbl 1124.26016
[6] Wu, S.: Some improvements of aczél’s inequality and popoviciu’s inequality, Comput. math. Appl. 56, 1196-1205 (2008) · Zbl 1155.26313 · doi:10.1016/j.camwa.2008.02.021
[7] Bellman, R.: On an inequality concerning an indefinite form, Amer. math. Monthly 63, 108-109 (1956) · Zbl 0070.27805 · doi:10.2307/2306434
[8] Diaz-Barrero, J. L.; Grau-Sanchez, M.; Popescu, P. G.: Refinements of aczél, popoviciu and Bellman’s inequalities, Comput. math. Appl. 56, 2356-2359 (2008) · Zbl 1165.26324 · doi:10.1016/j.camwa.2008.05.013