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Zbl 1218.26007
Anwar, M.; Jakšetić, J.; Pečarić, J.; Rehman, Atiq Ur
Exponential convexity, positive semi-definite matrices and fundamental inequalities. (English)
[J] J. Math. Inequal. 4, No. 2, 171-189 (2010). ISSN 1846-579X

Summary: The first two chapters of the classical book [{\it E. F. Beckenbach} and {\it R. Bellman}, Inequalities. Berlin-Göttingen-Heidelberg: Springer-Verlag (1961; Zbl 0097.26502)] on inequalities are devoted to fundamental inequalities and positive definiteness. In this paper we obtain results which give a connection between fundamental inequalities and positive definiteness using the notion of exponential convexity.

MSC 2000:: *26A51 Convexity, generalizations (one real variable)
26A46 Absolutely continuous functions (one real variable)
26A48 Monotonic functions, generalizations (one real variable)

Keywords: Jensen-Steffensen; Aczél; Mercer; Levinson inequalities; inequalities for power sums; exponentially convex functions; linear functionals

Citations: Zbl 0097.26502

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