The function (bx−ax)/x: Logarithmic convexity and applications to extended mean values-Reference-Cited by-同舟云学术

The function (bx−ax)/x: Logarithmic convexity and applications to extended mean values

Published:2011 Issue:4 Volume:25 Page:63-73
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Guo Bai-Ni¹,Feng Qi²

Affiliation:

1. School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, China

2. School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, China + Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City, China

Abstract

In the paper, we first prove the logarithmic convexity of the elementary function bx?ax/x, where x ? 0 and b > a > 0. Basing on this, we then provide a simple proof for Schur-convex properties of the extended mean values, and, finally, discover some convexity related to the extended mean values.

Publisher

National Library of Serbia

Subject

General Mathematics

Reference6 articles.

1. Steffensen pairs and associated inequalities

2. Generalization of Bernoulli polynomials

3. Extended Mean Values

4. Generalizations of Bernoulli numbers and polynomials

5. Logarithmic convexity of extended mean values

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