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On a generalization of Aczél’s inequality. (English) Zbl 1218.26030
Summary: We prove a generalization of Aczél’s inequality. The obtained inequalities extend some results established recently. We also give some comments on a recent result concerning the refinements of the generalized Aczél-Popoviciu’s inequality.

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, new applications of functional equations, Uspehi mat. Nauk (11) 69, No. 3, 3-68 (1956) · Zbl 0070.34903
[2] Wu, S.; Debnath, L.: Generalizations of aczél’s inequality and popoviciu’s inequality, Indian J. Pure appl. Math. 36, No. 2, 49-62 (2005) · Zbl 1083.26019
[3] Díaz-Barrerro, J. L.; Grau-Sánchez, 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
[4] 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
[5] Wu, S.; Debnath, L.: A new generalization of aczél’s inequality and its applications to an improvement of Bellman’s inequality, Appl. math. Lett. 21, 588-593 (2008) · Zbl 1134.26310 · doi:10.1016/j.aml.2007.07.010
[6] Hu, Z.; Xu, A.: Refinements of aczél and Bellman’s inequalities, Comput. math. Appl. 59, 3078-3083 (2010) · Zbl 1193.26018 · doi:10.1016/j.camwa.2010.02.027
[7] Yang, W.: Refinements of generalized aczél--popoviciu’s inequality and Bellman’s inequality, Comput. math. Appl. 59, 3570-3577 (2010) · Zbl 1197.26044 · doi:10.1016/j.camwa.2010.03.050
[8] Mitrinović, D. S.; Vasić, P. M.: Analytic inequalities, (1970) · Zbl 0213.22303