Open Access
May, 1984 Some Remarks About the Convolution of Unimodal Functions
Bela Uhrin
Ann. Probab. 12(2): 640-645 (May, 1984). DOI: 10.1214/aop/1176993312


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.


Download Citation

Bela Uhrin. "Some Remarks About the Convolution of Unimodal Functions." Ann. Probab. 12 (2) 640 - 645, May, 1984.


Published: May, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0554.60028
MathSciNet: MR735860
Digital Object Identifier: 10.1214/aop/1176993312

Primary: 26B99
Secondary: 26D15 , 60E15

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

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 2 • May, 1984
Back to Top