Sharp exponential type inequalities for the arc lemniscate sine function with applications

Sharp inequalities for tangent function with applications

In the article, we present new bounds for the function [Formula: see text] on the interval [Formula: see text] and find sharp estimations for the Sine integral and the Catalan constant based on a new monotonicity criterion for the quotient of power series, which refine the Redheffer and Becker-Stark type inequalities for tangent function.

New Inequalities of Shafer-Fink Type for Arc Hyperbolic Sine

Generalizations of Shafer-Fink-Type Inequalities for the Arc Sine Function

Wenhai Pan and Ling Zhu Department of Mathematics, Zhejiang Gongshang University, Hangzhou, Zhejiang 310018, China Correspondence should be addressed to Ling Zhu, [email protected] Received 29 December 2008; Revised 9 March 2009; Accepted 28 April 2009 Recommended by Sever Dragomir We give some generalizations of Shafer-Fink inequalities, and prove these inequalities by using a basic differen...

Sharp Jackson-type Inequalities for Approximations of Classes of Convolutions by Entire Functions of Exponential Type

In this paper, a new method is introduced for the proof of sharp Jacksontype inequalities for approximation of convolution classes of functions defined on the real line. These classes are approximated by linear operators with values in sets of entire functions of exponential type. In particular, a sharp Jackson-type inequality for the even-order derivatives of the conjugate function is proved. ...

Some extended Simpson-type inequalities and applications

‎In this paper‎, ‎we shall establish some extended Simpson-type inequalities‎ ‎for differentiable convex functions and differentiable concave functions‎ ‎which are connected with Hermite-Hadamard inequality‎. ‎Some error estimates‎ ‎for the midpoint‎, ‎trapezoidal and Simpson formula are also given‎.