Generalized Ostrowski, Opial and Hilbert-Pachpatte type inequalities for Banach algebra valued functions involving integer vectorial derivatives

Abstract

Using a generalized vectorial Taylor formula involving ordinary vector derivatives we establish mixed Ostrowski, Opial and Hilbert-Pachpatte type inequalities for several Banach algebra valued functions. The estimates are with respect to all norms kkp , 1p1. We Önish with applications.