Inequalities for Eigenfunctions of the P-Laplacian

Abstract

Abstract. Motivated by the work of P. Lindqvist, we study eigenfunctions of the one-dimensional p-Laplace operator, the sin p functions, and prove several inequalities for these and p-analogues of other trigonometric functions and their inverse functions. Similar inequalities are given also for the p-analogues of the hyperbolic functions and their inverses.

Turán type inequalities for generalized inverse trigonometric functions

“…Motivated by the work of Lindqvist, several authors have studies on the equalities and inequalities of the generalized trigonometric functions e.g, see [10,11,16,21,22,30,31] and their bibliography. Motivated by the many results on these generalized trigonometric functions, in this paper we make a contribution to the subject by showing some convexity properties [2,5] and Turán type inequalities for the inverse generalized trigonometric functions.…”

Functional inequalities for generalized inverse trigonometric and hyperbolic functions

“…These functions are the generalizations of the usual elementary inverse trigonometric and hyperbolic functions and are the inverse of the so-called generalized trigonometric and hyperbolic functions, introduced by P. Lindqvist [Li], see also [BE, EGL, LP, Ta] for more details. Recently, there has been a vivid interest on the generalized inverse trigonometric and hyperbolic functions, we refer to the papers [BBV,BBK,BS,BV1,BV2,JW,KVZ] and to the references therein. In this paper we make a contribution to the subject by showing various miscellaneous functional inequalities for the generalized inverse trigonometric and hyperbolic functions.…”

On the Inequalities for the Generalized Trigonometric Functions

“…In some cases this assumption will be relaxed to 1 < ≤ 2. We will adopt notation and definitions used in [5]. Let…”

“…Recently several inequalities for these families of functions have been obtained. We refer the interested reader to the following papers [3,5,[7][8][9]13] and to the references therein.…”

“…It is known that they are eigenfunctions of the Dirichlet problem for the one-dimensional -Laplacian. For more details concerning a recent progress in this rapidly growing area of functions theory the interested reader is referred to [1][2][3][4][5][6][7][8][9][10][11].…”