Integral inequalities for s-convex functions via generalized conformable fractional integral operators

We establish several basic inequalities versions of the Hermite-Hadamard type inequalities for GA− and GG−convexity for conformable fractional integrals. Several special cases are also discussed, which can be deduced from our main result.

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Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation

Mathematics ◽

10.3390/math10020204 ◽

2022 ◽

Vol 10 (2) ◽

pp. 204

Author(s):

Muhammad Bilal Khan ◽

Hatim Ghazi Zaini ◽

Savin Treanțǎ ◽

Mohamed S. Soliman ◽

Kamsing Nonlaopon

Keyword(s):

Convex Functions ◽

Fractional Integral ◽

Integral Operators ◽

Order Relation ◽

Integral Inequalities ◽

Fractional Integral Operators ◽

Invex Functions ◽

Left And Right ◽

Interval Valued

The concepts of convex and non-convex functions play a key role in the study of optimization. So, with the help of these ideas, some inequalities can also be established. Moreover, the principles of convexity and symmetry are inextricably linked. In the last two years, convexity and symmetry have emerged as a new field due to considerable association. In this paper, we study a new version of interval-valued functions (I-V·Fs), known as left and right χ-pre-invex interval-valued functions (LR-χ-pre-invex I-V·Fs). For this class of non-convex I-V·Fs, we derive numerous new dynamic inequalities interval Riemann–Liouville fractional integral operators. The applications of these repercussions are taken into account in a unique way. In addition, instructive instances are provided to aid our conclusions. Meanwhile, we’ll discuss a few specific examples that may be extrapolated from our primary findings.

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Refinements of Some Integral Inequalities for s , m -Convex Functions

Mathematical Problems in Engineering ◽

10.1155/2020/8878342 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13

Author(s):

Ghulam Farid ◽

Yu-Ming Chu ◽

Maja Andrić ◽

Chahn Yong Jung ◽

Josip Pečarić ◽

...

Keyword(s):

Convex Functions ◽

Fractional Integral ◽

Integral Operators ◽

Integral Inequalities ◽

Fractional Integral Operators

In this paper, the refinements of integral inequalities for all those types of convex functions are given which can be obtained from s , m -convex functions. These inequalities not only provide refinements of bounds for unified integral operators but also for various associated fractional integral operators containing Mittag–Leffler function. At the same time, presented results give generalizations of many known fractional integral inequalities.

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

Journal of Mathematics ◽

10.1155/2020/8245324 ◽

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.

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

Filomat ◽

10.2298/fil1816595s ◽

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.

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Riemann-Liouville Fractional integral operators with respect to increasing functions and strongly $ (\alpha, m) $-convex functions

AIMS Mathematics ◽

10.3934/math.2021661 ◽

2021 ◽

Vol 6 (10) ◽

pp. 11403-11424

Author(s):

Ghulam Farid ◽

◽

Hafsa Yasmeen ◽

Hijaz Ahmad ◽

Chahn Yong Jung ◽

...

Keyword(s):

Convex Functions ◽

Fractional Integral ◽

Integral Operators ◽

Integral Inequalities ◽

Fractional Integrals ◽

Fractional Integral Operators ◽

Strongly Convex ◽

Increasing Functions ◽

Integral Identities

<abstract><p>In this paper Hadamard type inequalities for strongly $ (\alpha, m) $-convex functions via generalized Riemann-Liouville fractional integrals are studied. These inequalities provide generalizations as well as refinements of several well known inequalities. The established results are further connected with fractional integral inequalities for Riemann-Liouville fractional integrals of convex, strongly convex and strongly $ m $-convex functions. By using two fractional integral identities some more Hadamard type inequalities are proved.</p></abstract>

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Certain Hermite-Hadamard type inequalities associated with conformable fractional integral operators

Creative Mathematics and Informatics ◽

10.37193/cmi.2017.03.09 ◽

2017 ◽

Vol 26 (3) ◽

pp. 321-330

Author(s):

ERHAN SET ◽

◽

BARIS CELIK ◽

Keyword(s):

Convex Functions ◽

Fractional Integral ◽

Integral Operators ◽

Fractional Integral Operators ◽

Conformable Fractional Integral

The aim of this article is to obtain some new Hermite-Hadamard type inequalities for convex functions via conformable fractional integral. The results presented here would provide extensions of those given in earlier works.

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Refinements of Some Integral Inequalities for φ -Convex Functions

Journal of Mathematics ◽

10.1155/2020/8825786 ◽

2020 ◽

Vol 2020 ◽

pp. 1-14

Author(s):

Moquddsa Zahra ◽

Yu-Ming Chu ◽

Ghulam Farid

Keyword(s):

Convex Function ◽

Convex Functions ◽

Fractional Integral ◽

Integral Operators ◽

Integral Inequalities ◽

Fractional Integral Operators

In this paper, we are interested to deal with unified integral operators for strongly φ -convex function. We will present refinements of bounds of these unified integral operators and use them to get associated results for fractional integral operators. Several known results are connected with particular assumptions.

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