اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn Jordan type inequalities for hyperbolic functions
75
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
This paper deals with some inequalities for trigonometric and hyperbolic functions such as the Jordan inequality and its generalizations. In particular, lower and upper bounds for functions such as (sin x)/x and x/(sinh x) are proved.
قيم البحث
اقرأ أيضاً
Famous Redheffers inequality is generalized to a class of anti-periodic functions. We apply the novel inequality to the generalized trigonometric functions and establish several Redheffer-type inequalities for these functions.
In this paper, we investigate the monotonicity and inequalities for some functions involving the arc lemniscate and the hyperbolic arc lemniscate functions. In particular, sharp Shafer-Fink type inequalities for the arc lemniscate and the hyperbolic arc lemniscate functions are proved.
We show that high-dimensional analogues of the sine function (more precisely, the d-dimensional polar sine and the d-th root of the d-dimensional hypersine) satisfy a simplex-type inequality in a real pre-Hilbert space H. Adopting the language of Dez
a and Rosenberg, we say that these d-dimensional sine functions are d-semimetrics. We also establish geometric identities for both the d-dimensional polar sine and the d-dimensional hypersine. We then show that when d=1 the underlying functional equation of the corresponding identity characterizes a generalized sine function. Finally, we show that the d-dimensional polar sine satisfies a relaxed simplex inequality of two controlling terms with high probability.
We revisit weighted Hardy-type inequalities employing an elementary ad hoc approach that yields explicit constants. We also discuss the infinite sequence of power weighted Birman-Hardy-Rellich-type inequalities and derive an operator-valued version thereof.
Using the Fourier analysis techniques on hyperbolic spaces and Greens function estimates, we confirm in this paper the conjecture given by the same authors in [43]. Namely, we prove that the sharp constant in the $frac{n-1}{2}$-th order Hardy-Sobolev
-Mazya inequality in the upper half space of dimension $n$ coincides with the best $frac{n-1}{2}$-th order Sobolev constant when $n$ is odd and $ngeq9$ (See Theorem 1.6). We will also establish a lower bound of the coefficient of the Hardy term for the $k-$th order Hardy-Sobolev-Mazya inequality in upper half space in the remaining cases of dimension $n$ and $k$-th order derivatives (see Theorem 1.7). Precise expressions and optimal bounds for Greens functions of the operator $ -Delta_{mathbb{H}}-frac{(n-1)^{2}}{4}$ on the hyperbolic space $mathbb{B}^n$ and operators of the product form are given, where $frac{(n-1)^{2}}{4}$ is the spectral gap for the Laplacian $-Delta_{mathbb{H}}$ on $mathbb{B}^n$. Finally, we give the precise expression and optimal pointwise bound of Greens function of the Paneitz and GJMS operators on hyperbolic space, which are of their independent interest (see Theorem 1.10).
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
