Ostrowski's Type Inequalities for the Complex Integral on Paths

Year 2020, Volume 3, Issue 4, 125 - 138, 01.12.2020

Sever DRAGOMIR

https://doi.org/10.33205/cma.798861

Abstract

In this paper we extend the Ostrowski inequality to the integral with respect to arc-length by providing upper bounds for the quantity |f(v)ℓ(γ)-∫_{γ}f(z)|dz|| under the assumptions that γ is a smooth path parametrized by z(t), t∈[a,b] with the length ℓ(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 for circular paths is also given. Several applications for circular paths and for some special functions of interest such as the exponential functions are also provided.

Keywords

Complex integral, Ostrowski inequality, Integrals on the paths

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