Abstract
In this paper we generalize the inequality
where
obtained by S.S. Dragomir for convex functions. We show that for the class of functions that we call superquadratic, strictly positive lower bounds of J n (f, x, p)—mJ n (f, x, q) and strictly negative upper bounds of J n (f, x, p)∔MJ n (f, x, q) exist when the functions are also nonnegative. We also provide cases where we can improve the bounds m and M for convex functions and superquadratic functions. Finally, an inequality related to the Čebyšev functional and superquadracity is also given.
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References
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© 2008 Birkhäuser Verlag Basel/Switzerland
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Abramovich, S., Dragomir, S.S. (2008). Normalized Jensen Functional, Superquadracity and Related Inequalities. In: Bandle, C., Losonczi, L., Gilányi, A., Páles, Z., Plum, M. (eds) Inequalities and Applications. International Series of Numerical Mathematics, vol 157. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-8773-0_20
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DOI: https://doi.org/10.1007/978-3-7643-8773-0_20
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