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Journal of Inequalities and Applications

, 2014:525

First Online: 23 December 2014Received: 08 October 2014Accepted: 11 December 2014

Abstract

In this paper, we find the least value r and the greatest value p such that the double inequality erf M p x , y ; λ ≤ H erf x , erf y ; λ ≤ erf M r x , y ; λ holds for all x , y ≥ 1 or 0 < x , y < 1 with 0 < λ < 1 , where erf x = 2 π ∫ 0 x e − t 2 d t , and M p x , y ; λ = λ x p + 1 − λ y p 1 - p p ≠ 0 and M 0 x , y ; λ = x λ y 1 − λ are, respectively, the error function, and weighted power mean.

MSC: 33B20, 26D15.

Keywordserror function power mean functional inequalities  Download fulltext PDF



Author: Yu-Ming Chu - Yong-Min Li - Wei-Feng Xia - Xiao-Hui Zhang

Source: https://link.springer.com/



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