## The Annals of Probability

- Ann. Probab.
- Volume 12, Number 2 (1984), 640-645.

### Some Remarks About the Convolution of Unimodal Functions

#### Abstract

In the note a new class of functions called $\alpha$-quasi-concave is introduced and it is proved that the convolution of two unimodal functions each having some additional concavity properties belongs to this class. Other results concerning the convolution of unimodal functions are also studied and the extensions of some of them are also given in the paper.

#### Article information

**Source**

Ann. Probab., Volume 12, Number 2 (1984), 640-645.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176993312

**Digital Object Identifier**

doi:10.1214/aop/1176993312

**Mathematical Reviews number (MathSciNet)**

MR735860

**Zentralblatt MATH identifier**

0554.60028

**JSTOR**

links.jstor.org

**Subjects**

Primary: 26B99: None of the above, but in this section

Secondary: 26D15: Inequalities for sums, series and integrals 60E15: Inequalities; stochastic orderings

**Keywords**

Quasiconcave unimodal $\alpha$-concave $\alpha$-quasi-concave $|alpha$-unimodal functions convolution integral inequalities

#### Citation

Uhrin, Bela. Some Remarks About the Convolution of Unimodal Functions. Ann. Probab. 12 (1984), no. 2, 640--645. doi:10.1214/aop/1176993312. https://projecteuclid.org/euclid.aop/1176993312