After considering a variant of the generalized mean value inequality of quasi-nearly subharmonic

functions, we consider certain invariance properties of quasinearly subharmonic functions. Koji´c

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 of these results by showing that in Rn, n ≥ 2, these both classes are invariant under

bi-Lipschitz mappings.

Author (s) Details

**Oleksiy Dovgoshey
**Department of Theory of Functions, Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, 84100, Slovyansk, Ukraine.

**Juhani Riihentaus
**Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FI-90014 Oulun Yliopisto, Finland and Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland.

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