By Pietro Cerone
This ebook is the 1st in a suite of study monographs which are dedicated to featuring fresh study, improvement and use of Mathematical Inequalities for certain features. the entire papers included within the ebook have peen peer-reviewed and canopy more than a few issues that come with either survey fabric of formerly released works in addition to new effects. In his presentation on distinctive capabilities approximations and boundaries through necessary illustration, Pietro Cerone utilises the classical Stevensen inequality and boundaries for the Ceby sev sensible to procure bounds for a few classical unique services. The technique depends on choosing bounds on integrals of goods of capabilities. The recommendations are used to acquire novel and worthwhile bounds for the Bessel functionality of the 1st style, the Beta functionality, the Zeta functionality and Mathieu sequence.
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Extra resources for Advances in inequalities for special functions
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Dragomir Proof. 8) exp (x2 − x1) f (x2 ) f (x2) f (x1) ≥ ≥ exp (x2 − x1) . 7). 2. 9) exp f (x + 1) f (x) f (x + 1) ≥ ≥ exp , f (x + 1) f (x) f (x) for any x ∈ [a, ∞). Another result is as follows. 3. Let f : I ⊆ R → (0, ∞) be a log-convex function which is differentiable on ˚ I. 10) (1 ≤) β [f (x1)] [f (x2)] f (x2) f (x1 ) ≤ exp αβ (x2 − x1) − f (αx1 + βx2) f (x2) f (x1 ) . Proof. 12) f (x2 ) f (x2 ) f (x2) = −α (x2 − x1) . 10). 4. 13) (1 ≤) β [f (x)] [f (x + h)] f (x + h) f (x) ≤ exp αβh − f (x + βh) f (x + h) f (x) for any α, β > 0 with α + β = 1.
No. 716-734 (1981), 22-24. N. , Cambridge University Press. T. N. Watson, A Course of Modern Analysis, Cambridge University Press, Cambridge, 1978. E. , In: Advances in Inequalities for Special Functions Editors: P. Cerone and S. S. Dragomir, pp. 37–65 ISBN 978-1-60021-919-1 c 2008 Nova Science Publishers, Inc. Inequalities for Positive Dirichlet Series P. Cerone and S. S. au Abstract. In this paper we survey some recent results of the authors concerning inequalities for Dirichlet series with positive terms.