scholarly journals Fractional Integral Inequalities for Some Convex Functions

2021 ◽  
Vol 104 (4) ◽  
pp. 14-27
Author(s):  
B.R. Bayraktar ◽  
◽  
A.Kh. Attaev ◽  
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Arithmetic Mean ◽  
Integral Inequalities ◽  
Power Mean ◽  
Logarithmic Mean ◽  
Real Numbers ◽  
Hadamard Inequality ◽  
Special Means

In this paper, we obtained several new integral inequalities using fractional Riemann-Liouville integrals for convex s-Godunova-Levin functions in the second sense and for quasi-convex functions. The results were gained by applying the double Hermite-Hadamard inequality, the classical Holder inequalities, the power mean, and weighted Holder inequalities. In particular, the application of the results for several special computing facilities is given. Some applications to special means for arbitrary real numbers: arithmetic mean, logarithmic mean, and generalized log-mean, are provided.

scholarly journals New fractional identities, associated novel fractional inequalities with applications to means and error estimations for quadrature formulas

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Artion Kashuri ◽  
Kottakkaran Sooppy Nisar ◽  
Muhammad Zakria Javed ◽  
Sabah Iftikhar ◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Quadrature Formulas ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Error Estimations ◽  
Harmonic Convex ◽  
Integral Identities

AbstractIn this paper, the authors derive some new generalizations of fractional trapezium-like inequalities using the class of harmonic convex functions. Moreover, three new fractional integral identities are given, and on using them as auxiliary results some interesting integral inequalities are found. Finally, in order to show the efficiency of our main results, some applications to special means for different positive real numbers and error estimations for quadrature formulas are obtained.

Some new fractional integral inequalities for generalized relative semi-m-(r; h1, h2)-preinvex mappings via generalized Mittag-Leffler function

2019 ◽  
Vol 26 (1/2) ◽  
pp. 41-55 ◽  
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Positive Real ◽  
Invex Set ◽  
Special Means ◽  
Special Cases ◽  
Differentiable Mappings

The authors discover a new identity concerning differentiable mappings defined on m-invex set via fractional integrals. By using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized relative semi- m-(r;h1,h2)-preinvex mappings by involving generalized Mittag-Leffler function are presented. It is pointed out that some new special cases can be deduced from main results of the paper. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.

scholarly journals Fejér type integral inequalities related with geometrically-arithmetically convex functions with applications

2019 ◽  
Vol 23 (1) ◽  
pp. 51-64
Author(s):  
S. S. Dragomir ◽  
M. A. Latif ◽  
E. Momoniat
Keyword(s):  
Differentiable Function ◽  
Integral Inequality ◽  
Convex Functions ◽  
Symmetric Function ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Positive Real ◽  
Left Part ◽  
Special Means ◽  
Type Integral

A new identity involving a geometrically symmetric function and a differentiable function is established. Some new Fejér type integral inequalities, connected with the left part of Hermite–Hadamard type inequalities for geometrically-arithmetically convex functions, are presented by using the Hölder integral inequality and the notion of geometrically-arithmetically convexity. Applications of our results to special means of positive real numbers are given.

scholarly journals Generalized Hadamard Fractional Integral Inequalities for Strongly s , m -Convex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Chao Miao ◽  
Ghulam Farid ◽  
Hafsa Yasmeen ◽  
Yanhua Bian
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Hadamard Inequality ◽  
Hadamard Fractional Integral

This article deals with Hadamard inequalities for strongly s , m -convex functions using generalized Riemann–Liouville fractional integrals. Several generalized fractional versions of the Hadamard inequality are presented; we also provide refinements of many known results which have been published in recent years.

scholarly journals Some Fejér type integral inequalities for geometrically-arithmetically-convex functions with applications

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2193-2206 ◽  
Author(s):  
Muhammad Latif ◽  
Sever Dragomir ◽  
Ebrahim Momoniat
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Symmetric Functions ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Type Integral

In this paper, the notion of geometrically symmetric functions is introduced. A new identity involving geometrically symmetric functions is established, and by using the obtained identity, the H?lder integral inequality and the notion of geometrically-arithmetically convexity, some new Fej?r type integral inequalities are presented. Applications of our results to special means of positive real numbers are given as well.

scholarly journals Hermite-Hadamard like inequalities for fractional integral operator via convexity and quasi-convexity with their applications

2021 ◽  
Vol 7 (3) ◽  
pp. 3418-3439
Author(s):  
Jamshed Nasir ◽  
◽  
Shahid Qaisar ◽  
Saad Ihsan Butt ◽  
Hassen Aydi ◽  
...  
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Bessel Functions ◽  
Fractional Operator ◽  
Real Numbers ◽  
Hadamard Inequality ◽  
Special Means ◽  
Special Cases ◽  
Derivatives Of ◽  
Quasi Convexity

<abstract><p>Since the supposed Hermite-Hadamard inequality for a convex function was discussed, its expansions, refinements, and variations, which are called Hermite-Hadamard type inequalities, have been widely explored. The main objective of this article is to acquire new Hermite-Hadamard type inequalities employing the Riemann-Liouville fractional operator for functions whose third derivatives of absolute values are convex and quasi-convex in nature. Some special cases of the newly presented results are discussed as well. As applications, several estimates concerning Bessel functions and special means of real numbers are illustrated.</p></abstract>

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 Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified h -Convex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Xiaobin Wang ◽  
Muhammad Shoaib Saleem ◽  
Kiran Naseem Aslam ◽  
Xingxing Wu ◽  
Tong Zhou
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
Convex Function ◽  
Convex Functions ◽  
Fractional Derivatives ◽  
Fractional Integral ◽  
Applied Mathematics ◽  
Fractional Integral Operator ◽  
Real Numbers ◽  
Special Means

The theory of convex functions plays an important role in engineering and applied mathematics. The Caputo–Fabrizio fractional derivatives are one of the important notions of fractional calculus. The aim of this paper is to present some properties of Caputo–Fabrizio fractional integral operator in the setting of h -convex function. We present some new Caputo–Fabrizio fractional estimates from Hermite–Hadamard-type inequalities. The results of this paper can be considered as the generalization and extension of many existing results of inequalities and convex functions. Moreover, we also present some application of our results to special means of real numbers.

Integral inequalities in a generalized context

2020 ◽  
Vol 57 (3) ◽  
pp. 312-320
Author(s):  
Péter Kórus ◽  
Luciano M. Lugo ◽  
Juan E. Nápoles Valdés
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Hadamard Inequality ◽  
Fractional Integral Operators

AbstractIn this paper we present different variants of the well-known Hermite–Hadamard inequality, in a generalized context. We consider general fractional integral operators for h-convex and r-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.

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