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By Pietro Cerone

This booklet is the 1st in a set of analysis monographs which are dedicated to featuring contemporary learn, improvement and use of Mathematical Inequalities for distinct services. all of the papers included within the publication have peen peer-reviewed and canopy a number themes that come with either survey fabric of formerly released works in addition to new effects. In his presentation on unique services approximations and boundaries through quintessential illustration, Pietro Cerone utilises the classical Stevensen inequality and boundaries for the Ceby sev practical to procure bounds for a few classical exact services. The method depends on selecting bounds on integrals of goods of services. The recommendations are used to acquire novel and precious bounds for the Bessel functionality of the 1st type, the Beta functionality, the Zeta functionality and Mathieu sequence.

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Cerone and S. Dragomir, Generalisations of the Gr¨ uss, Chebychev and Lupa¸s inequalities for integrals over different intervals, Int. J. Appl. , 6(2) (2001), 117-128. [22] P. S. Dragomir, On some inequalities arising from Montgomery’s identity, J. Comput. Anal. , 5(4) (2003), 341-362. [23] P. S. Dragomir, On some inequalities for the expectation and variance, Korean J. Comput. Appl. , 8(2) (2001), 357-380. [24] P. Cerone and C. Lenard, On integral forms of generalised Mathieu series, J. Inequal.

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. Applications for the Zeta function are also provided.

17) m− 1 2 m ψ (2kj ) ≤ j=1 + 1≤i

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