Exponential trigonometric convex functions and Hermite-Hadamard type inequalities
type: Item
instance of: scholarly article
title: Exponential trigonometric convex functions and Hermite-Hadamard type inequalities
zbMATH Open document ID: 1479.26011
author: Imdat İşcan
author: Mohamed Jleli
author: Mahir Kadakal
author: Praveen Agarwal
published in: Mathematica Slovaca
publication date: 2021-12-03T00:00:00Z
review text: In this paper, the authors introduce a new class of exponential trigonometric convex functions and define it as follows: A function \(f : I \subset \mathbb{R} \to \mathbb{R}\) is called an exponential trigonometric convex function if for every \(a,b \in I, t\in [0,1],\) \[ f(ta + (1-t)b)\le \frac{\sin\frac{\pi t}{2}}{e^{1-t}}f(a)+\frac{\cos\frac{\pi t}{2}}{e^t}f(b).\] The algebraic properties of this new class of functions are studied and well discussed. Using this newly introduced class of functions, the authors derive and prove the Hermite-Hadamard-type inequalities for this class of functions. Furthermore, some refinements of the Hermite-Hadamard-type inequalities for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, are shown to be exponential trigonometric convex function.
reviewed by: James A. Oguntuase
Mathematics Subject Classification ID: 26A51
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 7438324
zbMATH Keywords: convex function
zbMATH Keywords: trigonometric convex function
zbMATH Keywords: exponential trigonometric convex functions
zbMATH Keywords: Hermite-Hadamard inequality
zbMATH Keywords: Hölder-İşcan inequality
zbMATH Keywords: improved power-mean inequality
MaRDI profile type: Publication
full work available at URL: ms-2017-0410
OpenAlex ID: W3129163860
Wikidata QID: Q115514319
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DOI: 10.1515/MS-2017-0410
description: scientific article; zbMATH DE number 7438324