On Shafer-Fink-Type Inequality

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.

New Inequalities of Shafer-Fink Type for Arc Hyperbolic Sine

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) .

An Application of Λ-method on Shafer-fink’s Inequality

In the paper λ-method Mitrinovi´c-Vasi´c is applied aiming to improve Fink's inequality, and Shafer's inequality for arcus sinus function is observed. In monography [1, p. 247] Shafer's inequality is stated: (1) 3x 2 + √ 1 − x 2 ≤ asin x (0 ≤ x ≤ 1). The equality holds only for x = 0. In paper [2] Fink has proved the inequality: (2) asin x ≤ πx 2 + √ 1 − x 2 (0 ≤ x ≤ 1). The equality holds at b...

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...