Remarks on a main inequality for several special functions |
| |
Authors: | Mohammed Mesk |
| |
Institution: | 1. Département d'écologie et Environnement, Université de Tlemcen, Tlemcen, Algeria;2. Laboratoire d'Analyse Non Linéaire et Mathématiques Appliquées, Département de mathematiques, Université de Tlemcen, Tlemcen, Algeria |
| |
Abstract: | It is shown that the main inequality for several special functions derived in Masjed-Jamei M. A main inequality for several special functions. Comput Math Appl. 2010;60:1280–1289] can be put in a concise form, and that the main inequalities of the first kind Bessel function, Laplace and Fourier transforms are not valid as presented in the aforementioned paper. To provide alternative inequalities, we give a generalization, being in some cases an improvement, of the Cauchy–Bunyakovsky–Schwarz inequality which can be applied to real functions not necessarily of constant sign. The corresponding discrete inequality is also obtained, which we use to improve the inequalities of the Riemann zeta and the generalized Hurwitz–Lerch zeta functions. Finally, from the main concise inequality, we derive a Turán-type inequality. |
| |
Keywords: | A generalization of Cauchy–Bunyakovsky–Schwarz inequality classical special functions Fourier cosine and sine integral transforms Riemann zeta function generalized Hurwitz–Lerch zeta function Turán-type inequality |
|
|