<abstract xmlns="http://www.w3.org/1999/xhtml"> 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. </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.

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

Department of Mathematics and Computer Sciences Aurel Vlaicu University of Arad Bd. Revoluției nr.77, Arad, România

Department of Computer Sciences West University of Timișoara, Vasile Pârvan nr. 4, Timișoara, România

Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

The class of (k; h1; h2)-convex functions is introduced, together with some particular classes of corresponding generalized convex dominated functions. Few...

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

Published Online: Dec 12, 2015

Page range: 19 - 35

Received: Dec 29, 2014

Accepted: Mar 23, 2015

DOI: https://doi.org/10.1515/awutm-2015-0002

Keywords
generalized convex function, convex-dominated function, Bernstein-Doetsch theorem, Hermite- Hadamard’s inequality, regularity properties

© Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Dec 12, 2015

Page range: 19 - 35

Received: Dec 29, 2014

Accepted: Mar 23, 2015

DOI: https://doi.org/10.1515/awutm-2015-0002

Keywordsgeneralized convex function, convex-dominated function, Bernstein-Doetsch theorem, Hermite- Hadamard’s inequality, regularity properties

© Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Keywords
generalized convex function, convex-dominated function, Bernstein-Doetsch theorem, Hermite- Hadamard’s inequality, regularity properties