Certain generalized fractional integral inequalities

In this paper, the authors defined a new general class of functions, the so-called strongly (h1,h2)-nonconvex function involving F??,?(?) (Raina function). Utilizing this, some Hermite-Hadamard type integral inequalities via generalized fractional integral operator are obtained. Some new results as a special cases are given as well.

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Some generalized fractional integral inequalities with nonsingular function as a kernel

AIMS Mathematics ◽

10.3934/math.2021201 ◽

2021 ◽

Vol 6 (4) ◽

pp. 3352-3377

Author(s):

Shahid Mubeen ◽

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Rana Safdar Ali ◽

Iqra Nayab ◽

Gauhar Rahman ◽

...

Keyword(s):

Fractional Integral ◽

Integral Inequalities ◽

Generalized Fractional Integral

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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 generalized fractional integral inequalities for twice differentiable convex functions

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.112740 ◽

2020 ◽

Vol 372 ◽

pp. 112740 ◽

Cited By ~ 17

Author(s):

Pshtiwan Othman Mohammed ◽

Mehmet Zeki Sarikaya

Keyword(s):

Convex Functions ◽

Fractional Integral ◽

Integral Inequalities ◽

Generalized Fractional Integral

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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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A Generalized Fejér-Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results

10.20944/preprints201806.0089.v1 ◽

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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