International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 382179, 8 pages
doi:10.1155/2010/382179
Research Article

Bi-Lipschitz Mappings and Quasinearly Subharmonic Functions

Oleksiy Dovgoshey1 and Juhani Riihentaus2

1Institute of Applied Mathematics and Mechanics, NASU, R. Luxemburg Street 74, Donetsk 83114, Ukraine
2Department of Physics and Mathematics, University of Joensuu, P.O. Box 111, 80101 Joensuu, Finland

Received 30 November 2009; Accepted 25 December 2009

Academic Editor: Stanisława R. Kanas

Copyright © 2010 Oleksiy Dovgoshey and Juhani Riihentaus. 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.

Abstract

After considering a variant of the generalized mean value inequality of quasinearly subharmonic functions, we consider certain invariance properties of quasinearly subharmonic functions. Kojić has shown that in the plane case both the class of quasinearly subharmonic functions and the class of regularly oscillating functions are invariant under conformal mappings. We give partial generalizations to her results by showing that in ℝn, n≥2, these both classes are invariant under bi-Lipschitz mappings.