TRAPEZIUM-LIKE INEQUALITIES INVOLVING K-TH ORDER DIFFERENTIABLE RΓ-CONVEX FUNCTIONS AND APPLICATIONS

Miguel Vivas-Cortez; Muhammad Uzair Awan; Sadia Talib; Muhammad Aslam Noor; Khalida Inayat Noor

doi:10.3390/sym14030448

TRAPEZIUM-LIKE INEQUALITIES INVOLVING K-TH ORDER DIFFERENTIABLE RΓ-CONVEX FUNCTIONS AND APPLICATIONS

Miguel Vivas-Cortez, Muhammad Uzair Awan, Sadia Talib, Muhammad Aslam Noor, Khalida Inayat Noor

Faculty of Exact and Natural Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We introduce the class of R_γ-convex functions and discuss that it relates to some other classes of convexity. We study the class of R_γ-convex functions in the perspective of trapezium-like inequalities, for which we also derive a new integral identity involving a k-th order differentiable function. In order to show the significance of our results, we also discuss several special cases and offer some interesting applications.

Original language	English
Article number	448
Journal	Symmetry
Volume	14
Issue number	3
DOIs	https://doi.org/10.3390/sym14030448
State	Published - 23 Feb 2022

Bibliographical note

Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.

Funding

Funding: This research was funded by Dirección de Investigación from Pontificia Universidad Católica del Ecuador in the research project entitled, “Some integrals inequalities and generalized convexity” (Algunas desigualdades integrales para funciones con algún tipo de convexidad generalizada y aplicaciones).

Keywords

R-convex functions
convex
k-times differentiable
means
trapezium inequalities

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10.3390/sym14030448

Cite this

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abstract = "We introduce the class of Rγ-convex functions and discuss that it relates to some other classes of convexity. We study the class of Rγ-convex functions in the perspective of trapezium-like inequalities, for which we also derive a new integral identity involving a k-th order differentiable function. In order to show the significance of our results, we also discuss several special cases and offer some interesting applications.",

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AU - Talib, Sadia

AU - Noor, Muhammad Aslam

AU - Noor, Khalida Inayat

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AB - We introduce the class of Rγ-convex functions and discuss that it relates to some other classes of convexity. We study the class of Rγ-convex functions in the perspective of trapezium-like inequalities, for which we also derive a new integral identity involving a k-th order differentiable function. In order to show the significance of our results, we also discuss several special cases and offer some interesting applications.

KW - R-convex functions

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TRAPEZIUM-LIKE INEQUALITIES INVOLVING K-TH ORDER DIFFERENTIABLE RΓ-CONVEX FUNCTIONS AND APPLICATIONS

Abstract

Bibliographical note

Funding

Keywords

Access to Document

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