Fink’s Identity and Related Inequalities

Abstract

In this thesis, we present some refinements of the majorization theorems by using Fink's identity. Further, we use Green's function of order two together with Fink's identity and present a refinement of the majorization-type inequality. In addition, we give some results related to the Lidstone polynomial for 2n and (2n+2)-convex functions. Finally, we present some identities and inequalities related to the Lidstone polynomial and the Green functions.