A refinement of Grüss inequality for the complex integral

Silvestru Sever Dragomir

doi:10.2478/gm-2020-0006

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A refinement of Grüss inequality for the complex integral

General Mathematics

Volume 28 (2020): Issue 1 (June 2020)

By: Silvestru Sever Dragomir

Open Access

|Jul 2020

Abstract

Assume that f and g are continuous on γ, γ ⊂ 𝔺 is a piecewise smooth path parametrized by z (t), t ∈ [a, b] from z (a) = u to z (b) = w with w ≠ u and the complex Čebyšev functional is defined by

$𝒟_{γ} (f, g) : = \frac{1}{w - u} \int_{γ} f (z) g (z) d z - \frac{1}{w - u} \int_{γ} f (z) d z \frac{1}{w - u} \int_{γ} g (z) d z .$ {{\cal D}_\gamma}\left({f,g} \right): = {1 \over {w - u}}\int_\gamma {f\left(z \right)} g\left(z \right)dz - {1 \over {w - u}}\int_\gamma {f\left(z \right)} dz{1 \over {w - u}}\int_\gamma {g\left(z \right)} dz.

In this paper we establish some Grüss type inequalities for 𝒟 (f, g) under some complex boundedness conditions for the functions f and g.

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Articles in this issue

DOI: https://doi.org/10.2478/gm-2020-0006 | Journal eISSN: 1584-3289 | Journal ISSN: 1221-5023

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Language: English

Page range: 67 - 83

Submitted on: Feb 13, 2020

Accepted on: Apr 22, 2020

Published on: Jul 31, 2020

Published by: Lucian Blaga University of Sibiu

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Complex integral,

Continuous functions,

Holomorphic functions,

Grüss inequality

Related subjects:

Mathematics,

Differential equations and dynamical systems,

Probability and statistics,

Numerical and computational mathematics,

Applied mathematics

© 2020 Silvestru Sever Dragomir, published by Lucian Blaga University of Sibiu
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 28 (2020): Issue 1 (June 2020)