Hadamard type inequalities via some Euler type identities - Euler bitrapezoid formulae

Abstract

Hadamard's inequalities are given, by using some Euler-type identities. A number of inequalities, for functions whose derivatives are either functions of bounded variation or Lipschitzian functions or functions in Lp-spaces, is proved by applying the Euler bitrapezoid formulae. The results are applied to obtain some error estimates for the bitrapezoid quadrature rules.