Research Article

HERMITE-HADAMARD AND HERMITE-HADAMARD-FEJER TYPE INEQUALITIES FOR (k, h)-CONVEX FUNCTION VIA KATUGAMPOLA FRACTIONAL INTEGRALS

Volume: 5 Number: 2 October 15, 2017
EN

HERMITE-HADAMARD AND HERMITE-HADAMARD-FEJER TYPE INEQUALITIES FOR (k, h)-CONVEX FUNCTION VIA KATUGAMPOLA FRACTIONAL INTEGRALS

Abstract

In this paper, we obtain some new Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for (k,h)-convex functions via Katugampola fractionals which are a generalization of Riemann-Liouville and the Hadamard fractional integrals in to a single form.

Keywords

References

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  2. [2] H. Chen, U.N. Katugampola, Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for generalized fractional integrals, J. Math. Anal. Appl., 446 (2017), 1274-1291.
  3. [3] Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1 (1) (2010), 51-58.
  4. [4] S.S. Dragomir and S. Fitzpatrick, The Hadamard's inequality for s-convex functions in the rst sense, Demonstratio Math, 31 (3) (1998), 633-642.
  5. [5] S.S. Dragomir and S. Fitzpatrick, The Hadamard's inequality for s-convex functions in the second sense, Demonstration Math, 32 (4) (1999), 687-696.
  6. [6] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000 (Online:http:rgma.vu.edu.au/monographs)
  7. [7] S.S. Dragomir, J. Pecaric , L.E. Person, Some inequalities of Hadamard type, Soochow J. Math., 21 (1995), 335-341.
  8. [8] L. Fejer, Über die Fourierreihen, II, Math. Naturwiss. Anz.Ungar.Akad. Wiss., 24 (1906), 369-390.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

ERHAN Set
Türkiye

Publication Date

October 15, 2017

Submission Date

June 6, 2017

Acceptance Date

October 12, 2017

Published in Issue

Year 2017 Volume: 5 Number: 2

APA
Set, E., & Karaoğlan, A. (2017). HERMITE-HADAMARD AND HERMITE-HADAMARD-FEJER TYPE INEQUALITIES FOR (k, h)-CONVEX FUNCTION VIA KATUGAMPOLA FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics, 5(2), 181-191. https://izlik.org/JA97HM94JT
AMA
1.Set E, Karaoğlan A. HERMITE-HADAMARD AND HERMITE-HADAMARD-FEJER TYPE INEQUALITIES FOR (k, h)-CONVEX FUNCTION VIA KATUGAMPOLA FRACTIONAL INTEGRALS. Konuralp J. Math. 2017;5(2):181-191. https://izlik.org/JA97HM94JT
Chicago
Set, ERHAN, and ALİ Karaoğlan. 2017. “HERMITE-HADAMARD AND HERMITE-HADAMARD-FEJER TYPE INEQUALITIES FOR (k, H)-CONVEX FUNCTION VIA KATUGAMPOLA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 5 (2): 181-91. https://izlik.org/JA97HM94JT.
EndNote
Set E, Karaoğlan A (October 1, 2017) HERMITE-HADAMARD AND HERMITE-HADAMARD-FEJER TYPE INEQUALITIES FOR (k, h)-CONVEX FUNCTION VIA KATUGAMPOLA FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics 5 2 181–191.
IEEE
[1]E. Set and A. Karaoğlan, “HERMITE-HADAMARD AND HERMITE-HADAMARD-FEJER TYPE INEQUALITIES FOR (k, h)-CONVEX FUNCTION VIA KATUGAMPOLA FRACTIONAL INTEGRALS”, Konuralp J. Math., vol. 5, no. 2, pp. 181–191, Oct. 2017, [Online]. Available: https://izlik.org/JA97HM94JT
ISNAD
Set, ERHAN - Karaoğlan, ALİ. “HERMITE-HADAMARD AND HERMITE-HADAMARD-FEJER TYPE INEQUALITIES FOR (k, H)-CONVEX FUNCTION VIA KATUGAMPOLA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 5/2 (October 1, 2017): 181-191. https://izlik.org/JA97HM94JT.
JAMA
1.Set E, Karaoğlan A. HERMITE-HADAMARD AND HERMITE-HADAMARD-FEJER TYPE INEQUALITIES FOR (k, h)-CONVEX FUNCTION VIA KATUGAMPOLA FRACTIONAL INTEGRALS. Konuralp J. Math. 2017;5:181–191.
MLA
Set, ERHAN, and ALİ Karaoğlan. “HERMITE-HADAMARD AND HERMITE-HADAMARD-FEJER TYPE INEQUALITIES FOR (k, H)-CONVEX FUNCTION VIA KATUGAMPOLA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics, vol. 5, no. 2, Oct. 2017, pp. 181-9, https://izlik.org/JA97HM94JT.
Vancouver
1.ERHAN Set, ALİ Karaoğlan. HERMITE-HADAMARD AND HERMITE-HADAMARD-FEJER TYPE INEQUALITIES FOR (k, h)-CONVEX FUNCTION VIA KATUGAMPOLA FRACTIONAL INTEGRALS. Konuralp J. Math. [Internet]. 2017 Oct. 1;5(2):181-9. Available from: https://izlik.org/JA97HM94JT
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