Journal of Applied Mathematics and Stochastic Analysis
Volume 2008 (2008), Article ID 760214, 6 pages
Research Article

Integral Averages of Two Generalizations of the Poisson Kernel by Haruki and Rassias

Serap Bulut

Kocaeli University, Civil Aviation College, Arslanbey Campus, 41285 Izmit, Turkey

Received 15 November 2007; Revised 13 January 2008; Accepted 17 January 2008

Academic Editor: John Rassias

Copyright © 2008 Serap Bulut. 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.


In 1997, Haruki and Rassias introduced two generalizations of the Poisson kernel in two dimensions and discussed integral formulas for them. Furthermore, they presented an open problem. In 1999, Kim gave a solution to that problem. Here, we give a solution to this open problem by means of a different method. The purpose of this paper is to give integral averages of two generalizations of the Poisson kernel, that is, we generalize the open problem.