New Hermite–Hadamard Type Inequalities Involving Non-Conformable Integral Operators

At present, inequalities have reached an outstanding theoretical and applied development and they are the methodological base of many mathematical processes. In particular, Hermite– Hadamard inequality has received considerable attention. In this paper, we prove some new results related to Hermite–Hadamard inequality via symmetric non-conformable integral operators.

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Integral inequalities in a generalized context

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/012.2020.57.3.1464 ◽

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.

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On Some Generalized Fractional Integral Inequalities for p-Convex Functions

Fractal and Fractional ◽

10.3390/fractalfract3020029 ◽

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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On Hermite-Hadamard type inequalities via fractional integral operators

Filomat ◽

10.2298/fil1903837t ◽

2019 ◽

Vol 33 (3) ◽

pp. 837-854

Author(s):

Tuba Tunç ◽

Mehmet Sarıkaya

Keyword(s):

Convex Functions ◽

Fractional Integral ◽

Integral Operators ◽

Hadamard Inequality ◽

Fractional Integral Operators

In this paper, we give new definitions related to fractional integral operators for two variables functions using the class of integral operators. We are interested to give the Hermite-Hadamard inequality for a rectangle in plane via convex functions on co-ordinates involving fractional integral operators.

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Boundedness of Fractional Integral Operators Containing Mittag-Leffler Function via Exponentially s-Convex Functions

Journal of Mathematics ◽

10.1155/2020/3584105 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Gang Hong ◽

G. Farid ◽

Waqas Nazeer ◽

S. B. Akbar ◽

J. Pečarić ◽

...

Keyword(s):

Convex Functions ◽

Fractional Integral ◽

Symmetric Functions ◽

Integral Operators ◽

Arbitrary Point ◽

Fractional Integrals ◽

Hadamard Inequality ◽

Operator Inequalities ◽

Fractional Integral Operators ◽

Exponentially Convex Functions

The main objective of this paper is to obtain the fractional integral operator inequalities which provide bounds of the sum of these operators at an arbitrary point. These inequalities are derived for s-exponentially convex functions. Furthermore, a Hadamard inequality is obtained for fractional integrals by using exponentially symmetric functions. The results of this paper contain several such consequences for known fractional integrals and functions which are convex, exponentially convex, and s-convex.

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Derivation of bounds of several kinds of operators via $(s,m)$-convexity

Advances in Difference Equations ◽

10.1186/s13662-019-2470-0 ◽

2020 ◽

Vol 2020 (1) ◽

Cited By ~ 4

Author(s):

Young Chel Kwun ◽

Ghulam Farid ◽

Shin Min Kang ◽

Babar Khan Bangash ◽

Saleem Ullah

Keyword(s):

Lower Bounds ◽

Convex Functions ◽

Integral Operators ◽

Upper And Lower Bounds ◽

Hadamard Inequality

AbstractThe objective of this paper is to derive the bounds of fractional and conformable integral operators for $(s,m)$(s,m)-convex functions in a unified form. Further, the upper and lower bounds of these operators are obtained in the form of a Hadamard inequality, and their various fractional versions are presented. Some connections with already known results are obtained.

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Derivation of Bounds of an Integral Operator via Exponentially Convex Functions

Journal of Mathematics ◽

10.1155/2020/2456463 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Hong Ye ◽

Ghulam Farid ◽

Babar Khan Bangash ◽

Lulu Cai

Keyword(s):

Integral Operator ◽

Lower Bounds ◽

Differentiable Function ◽

Convex Functions ◽

Integral Operators ◽

Compact Form ◽

Upper And Lower Bounds ◽

Hadamard Inequality ◽

Absolute Value ◽

Exponentially Convex Functions

In this paper, bounds of fractional and conformable integral operators are established in a compact form. By using exponentially convex functions, certain bounds of these operators are derived and further used to prove their boundedness and continuity. A modulus inequality is established for a differentiable function whose derivative in absolute value is exponentially convex. Upper and lower bounds of these operators are obtained in the form of a Hadamard inequality. Some particular cases of main results are also studied.

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On New Generalizations of Hermite-Hadamard Type Inequalities via Atangana-Baleanu Fractional Integral Operators

Axioms ◽

10.3390/axioms10030223 ◽

2021 ◽

Vol 10 (3) ◽

pp. 223

Author(s):

Erhan Set ◽

Ahmet Ocak Akdemir ◽

Ali Karaoǧlan ◽

Thabet Abdeljawad ◽

Wasfi Shatanawi

Keyword(s):

Applied Sciences ◽

Integral Operator ◽

Fractional Integral ◽

Integral Operators ◽

Fractional Integral Operator ◽

Fractional Operators ◽

Hadamard Inequality ◽

Fractional Integral Operators ◽

Inequality Theory ◽

Fractional Analysis

Fractional operators are one of the frequently used tools to obtain new generalizations of clasical inequalities in recent years and many new fractional operators are defined in the literature. This development in the field of fractional analysis has led to a new orientation in various branches of mathematics and in many of the applied sciences. Thanks to this orientation, it has brought a whole new dimension to the field of inequality theory as well as many other disciplines. In this study, a new lemma has been proved for the fractional integral operator defined by Atangana and Baleanu. Later with the help of this lemma and known inequalities such as Young, Jensen, Hölder, new generalizations of Hermite-Hadamard inequality are obtained. Many reduced corollaries about the main findings are presented for classical integrals.

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Fejér–Hadamard Type Inequalities for (α, h-m)-p-Convex Functions via Extended Generalized Fractional Integrals

Fractal and Fractional ◽

10.3390/fractalfract5040253 ◽

2021 ◽

Vol 5 (4) ◽

pp. 253

Author(s):

Ghulam Farid ◽

Muhammad Yussouf ◽

Kamsing Nonlaopon

Keyword(s):

Fractional Order ◽

Convex Functions ◽

Fractional Integral ◽

Integral Operators ◽

Fractional Integrals ◽

Weighted Version ◽

Hadamard Inequality ◽

Fractional Integral Operators ◽

Different Types ◽

Inequality Type

Integral operators of a fractional order containing the Mittag-Leffler function are important generalizations of classical Riemann–Liouville integrals. The inequalities that are extensively studied for fractional integral operators are the Hadamard type inequalities. The aim of this paper is to find new versions of the Fejér–Hadamard (weighted version of the Hadamard inequality) type inequalities for (α, h-m)-p-convex functions via extended generalized fractional integrals containing Mittag-Leffler functions. These inequalities hold simultaneously for different types of well-known convexities as well as for different kinds of fractional integrals. Hence, the presented results provide more generalized forms of the Hadamard type inequalities as compared to the inequalities that already exist in the literature.

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