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.

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.

scholarly journals Some Inequalities of Generalized p-Convex Functions concerning Raina’s Fractional Integral Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Changyue Chen ◽  
Muhammad Shoaib Sallem ◽  
Muhammad Sajid Zahoor
Keyword(s):  
Integral Operator ◽  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Applied Mathematics ◽  
Optimization Theory ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Fractional Integral Operators

Convex functions play an important role in pure and applied mathematics specially in optimization theory. In this paper, we will deal with well-known class of convex functions named as generalized p-convex functions. We develop Hermite–Hadamard-type inequalities for this class of convex function via Raina’s fractional integral operator.

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.

scholarly journals New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1753
Author(s):  
Saima Rashid ◽  
Aasma Khalid ◽  
Omar Bazighifan ◽  
Georgia Irina Oros
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Type Inequality ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Convex Mappings ◽  
Special Cases ◽  
Harmonically Convex Functions

Integral inequalities for ℘-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented for ℘-convex functions via generalised fractional integral operator. A novel parameterized auxiliary identity involving generalised fractional integral is proposed for differentiable mappings. By using auxiliary identity, we derive several Ostrowski type inequalities for functions whose absolute values are ℘-convex mappings. It is presented that the obtained outcomes exhibit classical convex and harmonically convex functions which have been verified using Riemann–Liouville fractional integral. Several generalisations and special cases are carried out to verify the robustness and efficiency of the suggested scheme in matrices and Fox–Wright generalised hypergeometric functions.

scholarly journals On Strongly Convex Functions via Caputo–Fabrizio-Type Fractional Integral and Some Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Qi Li ◽  
Muhammad Shoaib Saleem ◽  
Peiyu Yan ◽  
Muhammad Sajid Zahoor ◽  
Muhammad Imran
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
Convex Functions ◽  
Fractional Integral ◽  
Optimization Problems ◽  
Fractional Integral Operator ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
Special Means ◽  
New Inequalities

The theory of convex functions plays an important role in the study of optimization problems. The fractional calculus has been found the best to model physical and engineering processes. The aim of this paper is to study some properties of strongly convex functions via the Caputo–Fabrizio fractional integral operator. In this paper, we present Hermite–Hadamard-type inequalities for strongly convex functions via the Caputo–Fabrizio fractional integral operator. Some new inequalities of strongly convex functions involving the Caputo–Fabrizio fractional integral operator are also presented. Moreover, we present some applications of the proposed inequalities to special means.

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 New Hadamard-type inequalities via $(s,m_{1},m_{2})$-convex functions

2021 ◽  
Vol 31 (4) ◽  
pp. 597-612
Author(s):  
B. Bayraktar ◽  
S.I. Butt ◽  
Sh. Shaokat ◽  
J.E. Nápoles Valdés
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Class Of Functions

The article introduces a new concept of convexity of a function: $(s,m_{1},m_{2})$-convex functions. This class of functions combines a number of convexity types found in the literature. Some properties of $(s,m_{1},m_{2})$-convexities are established and simple examples of functions belonging to this class are given. On the basis of the proved identity, new integral inequalities of the Hadamard type are obtained in terms of the fractional integral operator. It is shown that these results give us, in particular, generalizations of a number of results available in the literature.

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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