An application of Lambda-method on inequalities of Shafer-Fink's type

Sharpening and generalizations of Shafer-Fink's double inequality for the arc sine function

In this paper, we sharpen and generalize Shafer-Fink's double inequality for the arc sine function.

Shafer-Fink type inequalities for arc lemniscate 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.

Sharpening and Generalizations of Shafer-Fink and Wilker Type Inequalities: a New Approach

In this paper we propose and prove some generalizations and sharpenings of certain inequalities of Wilker;'s and Shafer-Fink's type. Application of the Wu-Debnath theorem enabled us to prove some double sided inequalities.

λ方法在Shafer-Fink不等式上的应用

An application of lambda-method on Shafer-Fink's inequality

本文应用Mitrinovic-Vasic的λ方法改进Fink不等式，并研究了反正弦函数的Shafer不等式。

A generalization of the Shafer-Fink inequality

In this article we show a tecnique based on the Weierstrass product for the sine and cosine function and the bisection formula for the cotangent function that leads to a generalization of the classical Shafer-Fink inequality $ \frac{3 x}{1+2\sqrt{1+x^2}} < \arctan x < \frac{πx}{1+2\sqrt{1+x^2}}$. Other algebraic approximations are also shown, including one that follows from the Chebyshev expansion for the arctangent function in the interval $[-1,1]$.

Sharp Cusa type inequalities for trigonometric functions with two parameters

Let $\left( p,q\right) \mapsto β\left( p,q\right) $ be a function defined on $\mathbb{R}^{2}$. We determine the best or better $p,q$ such that the inequality% \begin{equation*} \left( \frac{\sin x}{x}\right) ^{p}<\left( >\right) 1-β\left( p,q\right) +β\left( p,q\right) \cos ^{q}x \end{equation*}% holds for $x\in \left( 0,π/2\right) $, and obtain a lot of new and sharp Cusa type inequalities for trigonometric functions. As applications, some new Shafer-Fink type and Carlson type inequalities for arc sine and arc cosine functions, and new inequalities for trigonometric means are established.