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MEAN VALUE TYPE INEQUALITIES FOR QUASINEARLY SUBHARMONIC FUNCTIONS

Published online by Cambridge University Press:  25 February 2013

OLEKSIY DOVGOSHEY  and
JUHANI RIIHENTAUS
OLEKSIY DOVGOSHEY
Affiliation:
Institute of Applied Mathematics and Mechanics of NASU, R. Luxemburg Str. 74, Donetsk 83114, Ukraine e-mail: aleksdov@mail.ru
JUHANI RIIHENTAUS
Affiliation:
Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland e-mail: juhani.riihentaus@gmail.com
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Abstract

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The mean value inequality is characteristic for upper semi-continuous functions to be subharmonic. Quasinearly subharmonic functions generalise subharmonic functions. We find the necessary and sufficient conditions under which subsets of balls are big enough for the characterisation of non-negative, quasinearly subharmonic functions by mean value inequalities. Similar result is obtained also for generalised mean value inequalities where, instead of balls, we consider arbitrary bounded sets, which have non-void interiors and instead of the volume of ball some functions depending on the radius of this ball.

Keywords

Primary 31B0531C05Secondary 31C45
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 2 , May 2013 , pp. 349 - 368
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013

References

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