The Annals of Probability

Some Remarks About the Convolution of Unimodal Functions

Bela Uhrin

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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


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