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 Some new generalizations of Ostrowski type inequalities for s-convex functions via fractional integral operators

Filomat ◽  
2018 ◽  
Vol 32 (16) ◽  
pp. 5595-5609
Author(s):  
Erhan Set
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Fractional Integral ◽  
Present Note ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Class Of Functions

Remarkably a lot of Ostrowski type inequalities involving various fractional integral operators have been investigated by many authors. Recently, Raina [34] introduced a new generalization of the Riemann-Liouville fractional integral operator involving a class of functions defined formally by F? ?,?(x)=??,k=0 ?(k)/?(?k + ?)xk. Using this fractional integral operator, in the present note, we establish some new fractional integral inequalities of Ostrowski type whose special cases are shown to yield corresponding inequalities associated with Riemann-Liouville fractional integral operators.

scholarly journals On generalization of Fejér type inequalities via fractional integral operators

Filomat ◽  
2018 ◽  
Vol 32 (16) ◽  
pp. 5537-5547 ◽  
Author(s):  
Erhan Set ◽  
Ahmet Akdemir ◽  
Barış Çelik
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Differentiable Mapping ◽  
Fractional Integral Operators

In this paper we first prove a new lemma for differentiable mapping via a fractional integral operator. Then, using lemma, we establish some new Hermite-Hadamard-Fejer type results for convex functions via fractional integral operators. The results presented here would provide extensions of those given in earlier works.

scholarly journals FRACTIONAL INTEGRAL OPERATORS IN NONHOMOGENEOUS SPACES

2009 ◽  
Vol 80 (2) ◽  
pp. 324-334 ◽  
Author(s):  
H. GUNAWAN ◽  
Y. SAWANO ◽  
I. SIHWANINGRUM
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Type Inequality ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Homogeneous Type ◽  
Fractional Integral Operators

AbstractWe discuss here the boundedness of the fractional integral operatorIαand its generalized version on generalized nonhomogeneous Morrey spaces. To prove the boundedness ofIα, we employ the boundedness of the so-called maximal fractional integral operatorIa,κ*. In addition, we prove an Olsen-type inequality, which is analogous to that in the case of homogeneous type.

scholarly journals Some estimations on continuous random variables for (k, s) −fractional integral operators

2020 ◽  
Vol 6 (1) ◽  
pp. 143-154
Author(s):  
Mohamed Houas
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Random Variables ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integral Operators

AbstractIn this work, we establish some new (k, s) −fractional integral inequalities of continuous random variables by using the (k, s) −Riemann-Liouville fractional integral operator.

scholarly journals Study of Fractional Integral Operators Containing Mittag-Leffler Functions via Strongly α , m -Convex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Yanliang Dong ◽  
Maryam Saddiqa ◽  
Saleem Ullah ◽  
Ghulam Farid
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operators

The main aim of this paper is to give refinement of bounds of fractional integral operators involving extended generalized Mittag-Leffler functions. A new definition, namely, strongly α , m -convex function is introduced to obtain improvements of bounds of fractional integral operators for convex, m -convex, and α , m -convex functions. The results of this paper will provide simultaneous generalizations as well as refinements of various published results.

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.

scholarly journals Sharp Weighted Bounds for Fractional Integral Operators in a Space of Homogeneous Type

2014 ◽  
Vol 114 (2) ◽  
pp. 226 ◽  
Author(s):  
Anna Kairema
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Operator Norm ◽  
Fractional Integral Operator ◽  
Weighted Spaces ◽  
Space Of Homogeneous Type ◽  
Homogeneous Type ◽  
Fractional Integral Operators ◽  
The Relationship

We consider a version of M. Riesz fractional integral operator on a space of homogeneous type and show an analogue of the well-known Hardy-Littlewood-Sobolev theorem in this context. In our main result, we investigate the dependence of the operator norm on weighted spaces on the weight constant, and find the relationship between these two quantities. It it shown that the estimate obtained is sharp in any given space of homogeneous type with infinitely many points. Our result generalizes the recent Euclidean result by Lacey, Moen, Pérez and Torres [21].

scholarly journals Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Chahn Yong Jung ◽  
Muhammad Yussouf ◽  
Yu-Ming Chu ◽  
Ghulam Farid ◽  
Shin Min Kang
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Generalized Fractional Integral ◽  
Harmonically Convex Functions ◽  
Hadamard Fractional Integral ◽  
Generalized Fractional Integral Operators

In this paper, we define a new function, namely, harmonically α , h − m -convex function, which unifies various kinds of harmonically convex functions. Generalized versions of the Hadamard and the Fejér–Hadamard fractional integral inequalities for harmonically α , h − m -convex functions via generalized fractional integral operators are proved. From presented results, a series of fractional integral inequalities can be obtained for harmonically convex, harmonically h − m -convex, harmonically α , m -convex, and related functions and for already known fractional integral operators.

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.

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