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Supplements to Known Inequalities for Some Special Functions

✍ Scribed by Carla Giordano; Andrea Laforgia; Josip Pečarić

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
106 KB
Volume
200
Category
Article
ISSN
0022-247X

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✦ Synopsis

We establish some inequalities for the Bessel functions of the first kind J x Ž .

Ž . and for the modified Bessel functions I x and K x . Some of these results are obtained using the method of Giordano and Laforgia which is based essentially on the arithmetic᎐geometric mean inequality. Other results are established as a consequence of the classical Holder and Gram inequalities.

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## 2 3 Let f z s z q a z q a z q иии be a normalized strongly close-to-convex 2 3 function of order ␣ ) 0 defined on the unit disk ‫.ބ‬ This means that there is a normalized convex univalent function and ␤ g ‫ޒ‬ such that X f z ␣ Ž .