Estimations of Levinson-type inequalities using novel 3-convex Green functions with Taylor’s formula.

The goal of this study is to derive the generalized Levinson-type inequalities in the form of Taylor representation for higher order convex functions. This study uses Taylor’s formula and several novel types of 3-convex Green functions, to establish the novel identities associated with Bullen-type inequalities for higher order convex functions. Moreover, various Levinson-type inequalities are proved for positive real weights using Green functions and Taylor’s formula. [ABSTRACT FROM AUTHOR]