Abstract:
The mean value type inequality is characteristic for upper semi-continuous functions to be subharmonic.
Quasinearly subharmonic functions generalize subharmonic functions. The necessary and sufficient conditions
under which subsets of balls are “big enough” for the characterization of non-negative, quasinearly subharmonic
functions by mean value inequalities are found. Similar result is obtained also for generalized 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 diameter of considering set.
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