Related papers: Sharpening and generalizations of Shafer-Fink's do…
In this paper, by a concise and elementary approach, we sharpen and generalize Shafer's inequality for the arc sine function, and some known results are extended and generalized.
In this paper, we sharpen and generalize Shafer's inequality for the arc tangent function. From this, some known results are refined.
In this paper, we sharpen and generalize Carlson's double inequality for the arc cosine function.
In this paper, we sharpen and generalize Carlson's double inequality for the arc cosine function.
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.
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…
In this paper we give some sharper refinements and generalizations of inequalities related to Shafer's inequality for the arctangent function, stated in Theorems 1, 2 and 4 in [1], by C. Mortici and H.M. Srivastava.
A generalization of the affine-geometric Wirtinger inequality for curves to hypersurfaces is given.
The inverse tangent function can be bounded by different inequalities, for example by Shafer's inequality. In this publication, we propose a new sharp double inequality, consisting of a lower and an upper bound, for the inverse tangent…
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…
In this paper, we provide a concise proof of Oppenheim's double inequality relating to the cosine and sine functions. In passing, we survey this topic.
In this article, we obtain two interesting general inequalities concerning Riemman sums of convex functions, which in particular, sharpen Alzer's inequality and give a suitable converse for it.
A generalization of Mercer inequality for h-convex function is presented. As application, a weighted generalization of triangle inequality is given.
In this paper we shall prove a sharpened version of the Finsler-Hadwiger inequality which is a strong generalization of Weitzenbock inequality. After that we give another refinement of this inequality and in the final part we provide some…
In this paper, we find some new sharp bounds for $\left(\sin x\right) /x$, which unify and refine Jordan, Adamovi\'{c}-Mitrinovi\'{c}and and Cusa's inequalities. As applications of main results, some new Shafer-Fink type inequalities for…
In the paper $\lambda$-method Mitrinovic-Vasic is applied aiming to improve Fink's inequality, and Shafer's inequality for arcus sinus function is observed.
Identities and inequalities for the cosine and sine functions are obtained.
Let $\left( p,q\right) \mapsto \beta \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)…
In this paper we propose a new method for sharpening and refinements of some trigonometric inequalities. We apply these ideas to some inequalities of Wilker-Cusa-Huygens's type.
The aim of the present paper is to give extensions of the cosine-sine functional equation.