On Shafer and Carlson Inequalities

Inequalities for Hyperbolic Functions and Their Applications

In the study by Zhu in 1 , a basic theorem is established and found to be a source of inequalities for circular functions, and these inequalities are extended by this basic theorem. In what follows we are going to present the counterpart of these results for the hyperbolic functions. In this paper, we first establish the following Cusa-type inequalities in exponential type for hyperbolic functi...

SHAFER–FINK TYPE INEQUALITIES FOR THE ELLIPTIC FUNCTION sn(u|k) A. MCD. MERCER

The inequalities of Shafer and Fink, namely, 3x 2 + √ 1 − x2 sin −1(x) πx 2 + √ 1 − x2 , x ∈ [0, 1) are generalized to similar inequalities for the elliptic function sn(u|k) .

Refinements and generalizations of some inequalities of Shafer-Fink’s type for the inverse sine function

In this paper, we give some sharper refinements and generalizations of inequalities related to Shafer-Fink's inequality for the inverse sine function stated in Theorems 1, 2, and 3 of Bercu (Math. Probl. Eng. 2017: Article ID 9237932, 2017).

One-dimensional Interpolation Inequalities, Carlson–landau Inequalities and Magnetic Schrödinger Operators

In this paper we prove refined first-order interpolation inequalities for periodic functions and give applications to various refinements of the Carlson–Landau-type inequalities and to magnetic Schrödinger operators. We also obtain Lieb-Thirring inequalities for magnetic Schrödinger operators on multi-dimensional cylinders.

New Inequalities of Shafer-Fink Type for Arc Hyperbolic Sine