Regularity properties and integral inequalities related to (k; h1; h2)-convexity of functions

Gabriela Cristescu; Mihail Găianu; Awan Muhammad Uzair

doi:10.1515/awutm-2015-0002

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Regularity properties and integral inequalities related to (k; h1; h2)-convexity of functions

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 53 (2015): Issue 1 (July 2015)

By: Gabriela Cristescu, Mihail Găianu and Awan Muhammad Uzair

Open Access

|Dec 2015

Abstract

The class of (k; h₁; h₂)-convex functions is introduced, together with some particular classes of corresponding generalized convex dominated functions. Few regularity properties of (k; h₁; h₂)-convex functions are proved by means of Bernstein-Doetsch type results. Also we find conditions in which every local minimizer of a (k; h₁; h₂)-convex function is global. Classes of (k; h₁; h₂)-convex functions, which allow integral upper bounds of Hermite-Hadamard type, are identified. Hermite-Hadamard type inequalities are also obtained in a particular class of the (k; h₁; h₂)- convex dominated functions.

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Articles in this issue

DOI: https://doi.org/10.1515/awutm-2015-0002 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293

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Language: English

Page range: 19 - 35

Submitted on: Dec 29, 2014

Accepted on: Mar 23, 2015

Published on: Dec 12, 2015

Published by: West University of Timisoara

In partnership with: Paradigm Publishing Services

Publication frequency: Volume open

Keywords:

generalized convex function,

convex-dominated function,

Bernstein-Doetsch theorem,

Hermite- Hadamard’s inequality,

regularity properties

Related subjects:

Mathematics,

General mathematics

© 2015 Gabriela Cristescu, Mihail Găianu, Awan Muhammad Uzair, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 53 (2015): Issue 1 (July 2015)