Refining the Submean Inequality for Subharmonic Functions
Asare-Tuah Anton *
Department of Mathematics, University of Ghana, Legon, Ghana.
Prempeh Edward
Department of Mathematics, Kwame Nkrumah University of Science and Technology (KNUST), Ghana.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Convex function, subharmonic function, superquadratic function, jensen's inequality, submean inequality and refined jensen's inequality.