scholarly journals A Generalized Hermite-Hadamard Inequality for Coordinated Convex Function and Some Associated Mappings

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Atiq Ur Rehman ◽  
Gulam Farid ◽  
Sidra Malik
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Hadamard Inequality

We have discussed the generalization of Hermite-Hadamard inequality introduced by Lupaş for convex functions on coordinates defined in a rectangle from the plane. Also we define that mappings are related to it and their properties are discussed.

scholarly journals On Hadamard Type Fractional Inequalities for Riemann–Liouville Integrals via a Generalized Convexity

2022 ◽  
Vol 6 (1) ◽  
pp. 28
Author(s):  
Tao Yan ◽  
Ghulam Farid ◽  
Hafsa Yasmeen ◽  
Chahn Yong Jung
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Generalized Convexity ◽  
Monotone Function ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Recent Past ◽  
Hadamard Inequality

In the literature of mathematical inequalities, convex functions of different kinds are used for the extension of classical Hadamard inequality. Fractional integral versions of the Hadamard inequality are also studied extensively by applying Riemann–Liouville fractional integrals. In this article, we define (α,h−m)-convex function with respect to a strictly monotone function that unifies several types of convexities defined in recent past. We establish fractional integral inequalities for this generalized convexity via Riemann–Liouville fractional integrals. The outcomes of this work contain compact formulas for fractional integral inequalities which generate results for different kinds of convex functions.

scholarly journals On Some Generalized Fractional Integral Inequalities for p-Convex Functions

2019 ◽  
Vol 3 (2) ◽  
pp. 29
Author(s):  
Seren Salaş ◽  
Yeter Erdaş ◽  
Tekin Toplu ◽  
Erhan Set
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Hadamard Inequality ◽  
Fractional Integral Operators ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

In this paper, firstly we have established a new generalization of Hermite–Hadamard inequality via p-convex function and fractional integral operators which generalize the Riemann–Liouville fractional integral operators introduced by Raina, Lun and Agarwal. Secondly, we proved a new identity involving this generalized fractional integral operators. Then, by using this identity, a new generalization of Hermite–Hadamard type inequalities for fractional integral are obtained.

Exponential trigonometric convex functions and Hermite-Hadamard type inequalities

2021 ◽  
Vol 71 (1) ◽  
pp. 43-56
Author(s):  
Mahir Kadakal ◽  
İmdat İşcan ◽  
Praveen Agarwal ◽  
Mohamed Jleli
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Power Mean ◽  
Hadamard Inequality ◽  
Absolute Value ◽  
First Derivative ◽  
Algebraic Properties ◽  
Class Of Functions

Abstract In this manuscript, we introduce and study the concept of exponential trigonometric convex functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for the newly introduced class of functions. We also obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is exponential trigonometric convex function. It has been shown that the result obtained with Hölder-İşcan and improved power-mean integral inequalities give better approximations than that obtained with Hölder and improved power-mean integral inequalities.

scholarly journals A Generalized Fejér-Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results

2018 ◽  
Author(s):  
Shin Min Kang ◽  
Ghulam Abbas ◽  
Ghulam Farid ◽  
Waqas Nazeer
Keyword(s):  
Integral Operator ◽  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Hadamard Inequality ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Harmonically Convex Functions

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η-convex function. Moreover, our results include several new and known results as special cases.

POST QUANTUM-HERMITE-HADAMARD INEQUALITIES FOR DIFFERENTIABLE CONVEX FUNCTIONS WITH A CRITICAL POINT

2021 ◽  
Vol 21 (2) ◽  
pp. 337-346
Author(s):  
GHAZALA GULSHAN ◽  
RASHIDA HUSSAIN ◽  
ASGHAR ALI
Keyword(s):  
Convex Function ◽  
Critical Point ◽  
Convex Functions ◽  
Hadamard Inequality ◽  
Left Hand ◽  
Special Values ◽  
Special Cases

In this study, we obtained some new post quantum-Hermite-Hadamard inequalities for differentiable convex function with critical point by using generalized (p, q)- Hermite-Hadamard Inequality. The perseverance of this article is to establish different results on the left-hand side of (p,q)-Hermite-Hadamard inequality for differentiable convex function along with critical point. Special cases were obtained for different (p, q)-Hermite Hadamard inequalies with the critical point c for some special values of q.

scholarly journals Hermite–Hadamard-type inequalities via n-polynomial exponential-type convexity and their applications

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Saad Ihsan Butt ◽  
Artion Kashuri ◽  
Muhammad Tariq ◽  
Jamshed Nasir ◽  
Adnan Aslam ◽  
...  
Keyword(s):  
Convex Function ◽  
Error Estimates ◽  
Exponential Type ◽  
Convex Functions ◽  
Type Inequality ◽  
Hadamard Inequality ◽  
Absolute Value ◽  
Special Means ◽  
Algebraic Properties

Abstract In this paper, we give and study the concept of n-polynomial $(s,m)$ ( s , m ) -exponential-type convex functions and some of their algebraic properties. We prove new generalization of Hermite–Hadamard-type inequality for the n-polynomial $(s,m)$ ( s , m ) -exponential-type convex function ψ. We also obtain some refinements of the Hermite–Hadamard inequality for functions whose first derivatives in absolute value at certain power are n-polynomial $(s,m)$ ( s , m ) -exponential-type convex. Some applications to special means and new error estimates for the trapezoid formula are given.

scholarly journals Hermite-Hadamard-Fejér Inequality Related to Generalized Convex Functions via Fractional Integrals

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
M. Rostamian Delavar ◽  
S. Mohammadi Aslani ◽  
M. De La Sen
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integrals ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Absolute Value ◽  
Fejér Inequality ◽  
The Absolute

This paper deals with Hermite-Hadamard-Fejér inequality for (η1,η2)-convex functions via fractional integrals. Some mid-point and trapezoid type inequalities related to Hermite-Hadamard inequality when the absolute value of derivative of considered function is (η1,η2)-convex functions are obtained. Furthermore, a refinement for classic Hermite-Hadamard inequality via fractional integrals is given when a positive (η1,η2)-convex function is increasing.

scholarly journals KETAKSAMAAN HERMITE-HADAMARD TERHADAP INTEGRAL RIEMANN-STIELTJES

2012 ◽  
Vol 4 (1) ◽  
pp. 59
Author(s):  
Denny Ivanal Hakim ◽  
Hendra Gunawan
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Closed Interval ◽  
Mean Value ◽  
Stieltjes Integral ◽  
Power Mean ◽  
Real Numbers ◽  
Positive Real ◽  
Hadamard Inequality

The Hermite-Hadamard inequality is an inequality for convex functions that gives an estimate for the integral mean value of a convex function on a closed interval by its value at the middle of interval and the average of its values at the endpoints. The Hermite-Hadamard inequality can be generalized by using the Riemann-Stieltjes integral mean value.  An application of the Hermite-Hadamard inequality with respect to Riemann-Stieltjes integral  for estimating the power mean of   positive real numbers by the aritmethic mean is given at the end of discussion.

scholarly journals The Hermite Hadamard Inequality on Hypercuboid

2019 ◽  
Vol 16 ◽  
pp. 8234-8246
Author(s):  
Mohammad W Alomari
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Hadamard Inequality

Given any a := (a1; a2,... ; an) and b := (b1; b2;... ; bn) in Rn. The n-fold convex function dened on [a; b], a; b 2 Rn with a < b is a convex function in each variable separately. In this work we prove an inequality of Hermite-Hadamard type for n-fold convex functions. Namely, we establish the inequality

scholarly journals Hermite–Hadamard-Type Inequalities for F -Convex Functions via Katugampola Fractional Integral

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Erhan Set ◽  
İlker Mumcu
Keyword(s):  
Integral Operator ◽  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Function Class ◽  
Relevant Information ◽  
Fractional Integral Operator ◽  
Hadamard Inequality ◽  
Katugampola Fractional Integral

This article is organized as follows: First, definitions, theorems, and other relevant information required to obtain the main results of the article are presented. Second, a new version of the Hermite–Hadamard inequality is proved for the F-convex function class using a fractional integral operator introduced by Katugampola. Finally, new fractional Hermite–Hadamard-type inequalities are given with the help of F-convexity.

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