Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 748929, 35 pages
New Limit Formulas for the Convolution of a Function with a Measure and Their Applications
Department of Mathematics and Computing, University of Pannonia, 8200 Veszprém, Egyetem u. 10, Hungary
Received 16 July 2008; Accepted 23 September 2008
Academic Editor: Martin J. Bohner
Copyright © 2008 István Győri and László Horváth. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Asymptotic behavior of a convolution of a function with a measure is investigated. Our results give conditions which ensure that the exact rate of the convolution function can be determined using a positive weight function related to the given function and measure. Many earlier related results are included and generalized. Our new limit formulas are applicable to subexponential functions, to tail equivalent distributions, and to polynomial-type convolutions, among others.