Hermite-Hadamard-Fej\ {e}r type inequalities for harmonically convex functions via fractional integrals

<abstract><p>In this paper, we prove some new Ostrowski type inequalities for differentiable harmonically convex functions using generalized fractional integrals. Since we are using generalized fractional integrals to establish these inequalities, therefore we obtain some new inequalities of Ostrowski type for Riemann-Liouville fractional integrals and $ k $-Riemann-Liouville fractional integrals in special cases. Finally, we give some applications to special means of real numbers for newly established inequalities.</p></abstract>

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New Riemann–Liouville fractional Hermite–Hadamard type inequalities for harmonically convex functions

Arabian Journal of Mathematics ◽

10.1007/s40065-019-0255-7 ◽

2019 ◽

Vol 9 (2) ◽

pp. 431-441

Author(s):

Zeynep Şanlı ◽

Mehmet Kunt ◽

Tuncay Köroğlu

Keyword(s):

Convex Functions ◽

Fractional Integrals ◽

Differentiable Functions ◽

Left And Right ◽

Harmonically Convex Functions

Abstract In this paper, we proved two new Riemann–Liouville fractional Hermite–Hadamard type inequalities for harmonically convex functions using the left and right fractional integrals independently. Also, we have two new Riemann–Liouville fractional trapezoidal type identities for differentiable functions. Using these identities, we obtained some new trapezoidal type inequalities for harmonically convex functions. Our results generalize the results given by İşcan (Hacet J Math Stat 46(6):935–942, 2014).

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Hermite-Hadamard-Fejér type inequalities for co-ordinated harmonically convex functions via Katugampola fractional integrals

Engineering and Applied Science Letters ◽

10.30538/psrp-easl2021.0067 ◽

2021 ◽

Vol 4 (2) ◽

pp. 12-28

Author(s):

Naila Mehreen ◽

◽

Matloob Anwar ◽

Keyword(s):

Convex Functions ◽

Fractional Integral ◽

Fractional Integrals ◽

One Dimension ◽

Harmonically Convex Functions ◽

Katugampola Fractional Integral

The aim of this paper is to establish the Hermite-Hadamard-Fejér type inequalities for co-ordinated harmonically convex functions via Katugampola fractional integral. We provide Hermite-Hadamard-Fejér inequalities for harmonically convex functions via Katugampola fractional integral in one dimension.

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Hadamard and Fejér–Hadamard Inequalities for Further Generalized Fractional Integrals Involving Mittag-Leffler Functions

Journal of Mathematics ◽

10.1155/2021/5589405 ◽

2021 ◽

Vol 2021 ◽

pp. 1-13

Author(s):

M. Yussouf ◽

G. Farid ◽

K. A. Khan ◽

Chahn Yong Jung

Keyword(s):

Convex Functions ◽

Fractional Integral ◽

Integral Inequalities ◽

Fractional Integrals ◽

Harmonically Convex Functions

In this paper, generalized versions of Hadamard and Fejér–Hadamard type fractional integral inequalities are obtained. By using generalized fractional integrals containing Mittag-Leffler functions, some well-known results for convex and harmonically convex functions are generalized. The results of this paper are connected with various published fractional integral inequalities.

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On new inequalities of Hermite–Hadamard–Fejer type for harmonically convex functions via fractional integrals

SpringerPlus ◽

10.1186/s40064-016-2215-4 ◽

2016 ◽

Vol 5 (1) ◽

Cited By ~ 11

Author(s):

Mehmet Kunt ◽

İmdat İşcan ◽

Nazlı Yazıcı ◽

Uğur Gözütok

Keyword(s):

Convex Functions ◽

Fractional Integrals ◽

Harmonically Convex Functions ◽

New Inequalities

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Extensions of Hermite–Hadamard inequalities for harmonically convex functions via generalized fractional integrals

Journal of Inequalities and Applications ◽

10.1186/s13660-021-02638-3 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Xue-Xiao You ◽

Muhammad Aamir Ali ◽

Hüseyin Budak ◽

Praveen Agarwal ◽

Yu-Ming Chu

Keyword(s):

Convex Functions ◽

Fractional Integrals ◽

Convexity Property ◽

Hadamard Inequality ◽

Harmonically Convex Functions ◽

Harmonic Convexity

AbstractIn the paper, the authors establish some new Hermite–Hadamard type inequalities for harmonically convex functions via generalized fractional integrals. Moreover, the authors prove extensions of the Hermite–Hadamard inequality for harmonically convex functions via generalized fractional integrals without using the harmonic convexity property for the functions. The results offered here are the refinements of the existing results for harmonically convex functions.

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