Research Article

Hermite-Hadamard Type Inequalities for Generalized Fractional Integrals via Strongly Convex Functions

Volume: 7 Number: 2 October 15, 2019
EN

Hermite-Hadamard Type Inequalities for Generalized Fractional Integrals via Strongly Convex Functions

Abstract

In this paper, the authors have obtained some new developments of Hermite-Hadamard type inequalities for generalized fractional integrals defined by Mubeen et. al. \cite{SSM}. In the last part of the article, some results are given with the help of the definition of many fractional integral arising from the generalization.

Keywords

References

  1. [1] A. Akkurt, M. E. Yıldırım and H. Yıldırım, On some Integral Inequalities for (k;h)􀀀Riemann-Liouville fractional integral, New Trends in Mathematical Sciences (NTMSCI), 4(1), (2016), 138-146.
  2. [2] B.T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions. Sov. Math. Dokl. 7, 72–75 (1966).
  3. [3] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Diferential Equations, Elsevier B.V., Amsterdam, Netherlands, 2006.
  4. [4] N. Merentes and K. Nikodem, Remarks on strongly convex functions. Aequ. Math. 80, 193–199 (2010).
  5. [5] S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives-Theory and Applications, Gordon and Breach, Linghorne, 1993.
  6. [6] S. Mubeen, S. Iqbal and M. Tomar, Hermite-Hadamard Type Inequalities via Fractional Integrals of a Function With Respect to Another Function and k􀀀parameter, J. Inequal. Math. Appl. 1 (2017), 1-9.
  7. [7] M. Zeki Sarikaya, E. Set, H. Yaldiz and N. Basak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, doi:10.1016/j.mcm.2011.12.048, 57 (2013) 2403–2407.
  8. [8] F. Ertugral, M. Zeki Sarıkaya and H. Budak, On Refinements of Hermite-Hadamard-Fejer Type Inequalities for Fractional Integral Operators, Applications and Applied Mathematics,Vol. 13, Issue 1 (June 2018), pp. 426-442.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Publication Date

October 15, 2019

Submission Date

February 15, 2018

Acceptance Date

April 30, 2019

Published in Issue

Year 2019 Volume: 7 Number: 2

APA
Gidergelmez, H. F., Akkurt, A., & Yıldırım, H. (2019). Hermite-Hadamard Type Inequalities for Generalized Fractional Integrals via Strongly Convex Functions. Konuralp Journal of Mathematics, 7(2), 268-273. https://izlik.org/JA78BD47YE
AMA
1.Gidergelmez HF, Akkurt A, Yıldırım H. Hermite-Hadamard Type Inequalities for Generalized Fractional Integrals via Strongly Convex Functions. Konuralp J. Math. 2019;7(2):268-273. https://izlik.org/JA78BD47YE
Chicago
Gidergelmez, Hasan Fehmi, Abdullah Akkurt, and Hüseyin Yıldırım. 2019. “Hermite-Hadamard Type Inequalities for Generalized Fractional Integrals via Strongly Convex Functions”. Konuralp Journal of Mathematics 7 (2): 268-73. https://izlik.org/JA78BD47YE.
EndNote
Gidergelmez HF, Akkurt A, Yıldırım H (October 1, 2019) Hermite-Hadamard Type Inequalities for Generalized Fractional Integrals via Strongly Convex Functions. Konuralp Journal of Mathematics 7 2 268–273.
IEEE
[1]H. F. Gidergelmez, A. Akkurt, and H. Yıldırım, “Hermite-Hadamard Type Inequalities for Generalized Fractional Integrals via Strongly Convex Functions”, Konuralp J. Math., vol. 7, no. 2, pp. 268–273, Oct. 2019, [Online]. Available: https://izlik.org/JA78BD47YE
ISNAD
Gidergelmez, Hasan Fehmi - Akkurt, Abdullah - Yıldırım, Hüseyin. “Hermite-Hadamard Type Inequalities for Generalized Fractional Integrals via Strongly Convex Functions”. Konuralp Journal of Mathematics 7/2 (October 1, 2019): 268-273. https://izlik.org/JA78BD47YE.
JAMA
1.Gidergelmez HF, Akkurt A, Yıldırım H. Hermite-Hadamard Type Inequalities for Generalized Fractional Integrals via Strongly Convex Functions. Konuralp J. Math. 2019;7:268–273.
MLA
Gidergelmez, Hasan Fehmi, et al. “Hermite-Hadamard Type Inequalities for Generalized Fractional Integrals via Strongly Convex Functions”. Konuralp Journal of Mathematics, vol. 7, no. 2, Oct. 2019, pp. 268-73, https://izlik.org/JA78BD47YE.
Vancouver
1.Hasan Fehmi Gidergelmez, Abdullah Akkurt, Hüseyin Yıldırım. Hermite-Hadamard Type Inequalities for Generalized Fractional Integrals via Strongly Convex Functions. Konuralp J. Math. [Internet]. 2019 Oct. 1;7(2):268-73. Available from: https://izlik.org/JA78BD47YE
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