Linear inequalities via extension of Montgomery identity and Weighted Hermite-Hadamard inequalities with and without Green Functions

Abstract

Weighted Hermite-Hadamard dual inequality in integral form is an important result as its left hand inequality is in fact Jensen inequality and right hand inequality is the Lah–Ribaric inequality. In this paper new linear inequalities are introduced via extension of Montgomery identity and weighted Hermite-Hadamard inequalities with and without Green functions in discrete and integral cases.