Refining the Submean Inequality for Subharmonic Functions
Asare-Tuah Anton, Prempeh Edward
Journal of Advances in Mathematics and Computer Science · pp. 1–10 · Published 17 Oct 2015
10.9734/BJMCS/2016/21851Abstract
It is known that the composition of a convex, increasing functional with a subharmonic function is subharmonic. In this paper we show that the composition of a superquadratic functional with a subharmonic function is subharmonic, with a sharper submean inequality. It is further demonstrated that the composition of an increasing convex functional with a nonnegative superquadratic functional with a subharmonic function is subharmonic, with a sharper submean inequality.
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