Ostrowski’s Type Inequalities for the Complex Integral on Paths

Abstract

In this paper, we extend the Ostrowski inequality to the integral with respect to arc-length by providingupper bounds for the quantity f (v) ` (γ) −Zγf (z) |dz| under the assumptions that γ is a smooth path parametrized by z (t) , t ∈ [a, b] with the length ` (γ) , u = z (a) ,v = z (x) with x ∈ (a, b) and w = z (b) while f is holomorphic in G, an open domain and γ ⊂ G. An application forcircular paths is also given.