Fractional Hermite-Hadamard inequalities containing generalized Mittag-Leffler function

Mihai, Marcela V.; Awan, Muhammad Uzair; Noor, Muhammad Aslam; Noor, Khalida İnayat

doi:10.1186/s13660-017-1543-4

Cited by 4 publications

(3 citation statements)

References 16 publications

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“…For some similar studies with this work about harmonically convex functions, readers can see [1,2,3,5,6,7,8,9,13,14,15,16,17,20] and references therein.…”

Section: Introductionmentioning

confidence: 86%

Improved Hermite Hadamard type inequalities for harmonically convex functions via Katugampola fractional integrals

Şanlı¹,

Köroğlu²,

Kunt³

2019

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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In this paper, we prove three new Katugampola fractional Hermite-Hadamard type inequalities for harmonically convex functions by using the left and the right fractional integrals independently. One of our Katugampola fractional Hermite-Hadamard type inequalities is better than given in [17]. Also, we give two new Katugampola fractional identities for di¤erentiable functions. By using these identities, we obtain some new trapezoidal type inequalities for harmonically convex functions. Our results generalize many results from earlier papers.

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“…For some similar studies with this work about harmonically convex functions, readers can see [1,2,3,5,6,7,8,9,13,14,15,16,17,20] and references therein.…”

Section: Introductionmentioning

confidence: 86%

Improved Hermite Hadamard type inequalities for harmonically convex functions via Katugampola fractional integrals

Şanlı¹,

Köroğlu²,

Kunt³

2019

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…More information related to the Mittag-Leffler functions and the corresponding fractional integral operators can be found in the literature [76][77][78].…”

Section: Introductionmentioning

confidence: 99%

Some new fractional integral inequalities for exponentially m-convex functions via extended generalized Mittag-Leffler function

et al. 2019

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“…In [4],İşcan gave Hermite-Hadamard type inequalities for harmonically convex functions as follows. For some similar studies with this work about harmonically convex functions, readers can see [1][2][3][4][5][6][8][9][10]13,14] and references therein.…”

mentioning

confidence: 99%

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

2019

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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 byİşcan (Hacet J Math Stat 46(6):935-942, 2014). Mathematics Subject Classification 26A51 • 26A33 • 26D10 for all x, y ∈ I and t ∈ [0, 1]. If the inequality in (1.2) is reversed, then f is said to be harmonically concave.

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Fractional Hermite-Hadamard inequalities containing generalized Mittag-Leffler function

Abstract: The objective of this paper is to establish some new refinements of fractional Hermite-Hadamard inequalities via a harmonically convex function with a kernel containing the generalized Mittag-Leffler function.

Cited by 4 publications

References 16 publications

Improved Hermite Hadamard type inequalities for harmonically convex functions via Katugampola fractional integrals

Improved Hermite Hadamard type inequalities for harmonically convex functions via Katugampola fractional integrals

Some new fractional integral inequalities for exponentially m-convex functions via extended generalized Mittag-Leffler function

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

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