The function $(b^x-a^x)/x$ : Logarithmic convexity and applications to extended mean values

preprint2009arXivOpen access

In the present paper, we first prove the logarithmic convexity of the elementary function $\frac{b^x-a^x}x$ , where $x\ne0$ 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.

Explore this paper’s authors, topics and related work.

Building this map preview

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Write a reviewWrite

No reviews yet.

Add a commentWrite

No comments yet.

The function $(b^x-a^x)/x$ : Logarithmic convexity and applications to extended mean values

Abstract

Connections

Building this map preview

Reviews 0

Discussion 0

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

Abstract

Connections

Building this map preview

Reviews 0

Discussion 0

The function $(b^x-a^x)/x$ : Logarithmic convexity and applications to extended mean values