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

Mumcu, İlker; Set, Erhan; Akdemir, Ahmet Ocak

doi:10.18514/mmn.2019.2722

Cited by 14 publications

(12 citation statements)

References 10 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%

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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%

“…Because of the wide application of Hermite-Hadamard type inequalities and fractional integrals, researchers extend their studies to Hermite-Hadamard type inequalities involving fractional integrals. The papers [3,8,9,13,14,15,17,20] are based on Hermite-Hadamard type inequalities involving several fractional integrals.…”

Section: De…nition 8 Let [A; B]mentioning

confidence: 99%

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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“…Therefore, many generalizations of different inequalities are studied via these fractional integrals. For example, Kermausuor [28] and Mumcu et al [29] generalized Ostrowski-type and Hermite-Hadamard type inequalities for harmonically convex functions, respectively. Tekin et al [30] proposed Hermite-Hadamard inequality for p-convex functions for Katugampola fractional integrals.…”

Section: Respectivelymentioning

confidence: 99%

New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals

Almutairi

Kılıçman

2020

Symmetry

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In this paper, a new identity for the generalized fractional integral is defined. Using this identity we studied a new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. This fractional integral generalizes Riemann-Liouville and Hadamard’s integral, which possess a symmetric property. We derive trapezoid and mid-point type inequalities connected to this generalized Hermite-Hadamard inequality.

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“…whereby I 1 , I 2 and I 3 are the first, second and third integrals in inequality (14). When calculating I 1 and I 2 , we get the following…”

Section: New Generalized Fractional Integrals Identity and New Integrmentioning

confidence: 99%

“…Therefore, many generalizations of different inequalities are studied via these fractional integrals. For example, Kermausuor [24] and Mumcu et al, [14] generalized Ostrowski-type and Hermite-Hadamard type inequalities for harmonically convex functions, respectively. Therefore, the aim of this paper is to generalize the Hermite-Hadamard inequality for generalized convex functions on fractal sets via Katugampola fractional integrals.…”

Section: Introductionmentioning

confidence: 99%

New Generalized the Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals

Almutairi¹,

Kılıçman²

2020

Preprint

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In this paper, a new identity for the generalized fractional integral is defined, through which new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. We derive trapezoid and mid-point type inequalities connected to these generalized Hermite-Hadamard inequality.

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

Abstract: In this work, firstly, we established Hermite-Hadamard's inequalities for harmonically convex functions via Katugampola fractional integrals. Then we give some Hermite-Hadamard type inequalities of these classes functions.

Cited by 14 publications

References 10 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

New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals

New Generalized the Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals

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