Extensions and improvements of Sherman’s and related inequalities for n-convex functions

Abstract

This paper gives extensions and improvements of Sherman's inequality for n-convex functions obtained by using new identities which involve Green's functions and Fink's identity. Moreover, extensions and improvements of Majorization inequality as well as Jensen's inequality are obtained as direct consequences. New inequalities between geometric, logarithmic and arithmetic means are also established.

Sherman’s inequality and its converse for strongly convex functions withapplications to generalizedf-divergences

“…Recently, Sherman's result has attracted the interest of several mathematicians (see [1][2][3][4][5], [12][13][14][15], [23][24][25][26][27][28][29][30]).…”