IMPROVED HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS VIA KATUGAMPOLA FRACTIONAL INTEGRALS

Zeynep Şanlı; Mehmet Kunt; Tuncay Köroğlu

IMPROVED HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS VIA KATUGAMPOLA FRACTIONAL INTEGRALS

Abstract

In this paper, we gave adjustments for some results in the paper [1], and proved three new Katugampola fractional Hermite-Hadamard type inequalities for 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 by Chen and Katugampola. Also, we gave two new Katugampola fractional identities for differentiable functions. By using these identities, we obtained some new trapezoidal type inequalities for convex functions. Our results generalize earlier results.

Keywords

References

[1] Chen, H., Katugampola, U. N., Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for generalized fractional integrals. J. Math. Anal. Appl. 446 (2017), 1274-1291.
[2] Dragomir, S. S., Agarwal, R. P., Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11(5) (1998), 91-95.
[3] Hadamard, J., Etude sur les proprietes des fonctions entieres et en particulier d'une fonction consideree par Riemann, J. Math. Pures Appl., 58 (1893), 171-215.
[4] Hermite, Ch., Sur deux limites d'une integrale definie, Mathesis, 3 (1883), 82-83.
[5] Katugampola, U. N., New approach to generalized fractional integral, Appl. Math. Comput. 218 (3) (2011) 860-865.
[6] Katugampola, U. N., Mellin transforms of generalized fractional integrals and derivatives, Appl. Math. Comput. 257 (2015) 566-580.
[7] Kilbas, A. A., Srivastava, H. M., Trujillo, J. J., Theory and applications of fractional differential equations. Elsevier, Amsterdam (2006).
[8] Kunt, M., Karapınar, D., Turhan, S., İşcan, İ., The left Rieaman-Liouville fractional Hermite-Hadamard type inequalities for convex functions, Mathematica Slovaca (2019) (Accepted for publication).

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Zeynep Şanlı This is me
0000-0002-1564-2634
Türkiye

Mehmet Kunt This is me
0000-0002-8730-5370
Türkiye

Tuncay Köroğlu This is me
0000-0002-1341-1074
Türkiye

Publication Date

June 1, 2019

Submission Date

April 9, 2018

Acceptance Date

March 11, 2019

Published in Issue

Year 2019 Volume: 37 Number: 2

IZ

https://izlik.org/JA66CN73PA

Cite

RIS / Bibtex

APA

Şanlı, Z., Kunt, M., & Köroğlu, T. (2019). IMPROVED HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS VIA KATUGAMPOLA FRACTIONAL INTEGRALS. Sigma Journal of Engineering and Natural Sciences, 37(2), 461-474. https://izlik.org/JA66CN73PA

AMA

1.Şanlı Z, Kunt M, Köroğlu T. IMPROVED HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS VIA KATUGAMPOLA FRACTIONAL INTEGRALS. SIGMA. 2019;37(2):461-474. https://izlik.org/JA66CN73PA

Chicago

Şanlı, Zeynep, Mehmet Kunt, and Tuncay Köroğlu. 2019. “IMPROVED HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS VIA KATUGAMPOLA FRACTIONAL INTEGRALS”. Sigma Journal of Engineering and Natural Sciences 37 (2): 461-74. https://izlik.org/JA66CN73PA.

EndNote

Şanlı Z, Kunt M, Köroğlu T (June 1, 2019) IMPROVED HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS VIA KATUGAMPOLA FRACTIONAL INTEGRALS. Sigma Journal of Engineering and Natural Sciences 37 2 461–474.

IEEE

[1]Z. Şanlı, M. Kunt, and T. Köroğlu, “IMPROVED HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS VIA KATUGAMPOLA FRACTIONAL INTEGRALS”, SIGMA, vol. 37, no. 2, pp. 461–474, June 2019, [Online]. Available: https://izlik.org/JA66CN73PA

ISNAD

Şanlı, Zeynep - Kunt, Mehmet - Köroğlu, Tuncay. “IMPROVED HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS VIA KATUGAMPOLA FRACTIONAL INTEGRALS”. Sigma Journal of Engineering and Natural Sciences 37/2 (June 1, 2019): 461-474. https://izlik.org/JA66CN73PA.

JAMA

1.Şanlı Z, Kunt M, Köroğlu T. IMPROVED HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS VIA KATUGAMPOLA FRACTIONAL INTEGRALS. SIGMA. 2019;37:461–474.

MLA

Şanlı, Zeynep, et al. “IMPROVED HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS VIA KATUGAMPOLA FRACTIONAL INTEGRALS”. Sigma Journal of Engineering and Natural Sciences, vol. 37, no. 2, June 2019, pp. 461-74, https://izlik.org/JA66CN73PA.

Vancouver

1.Zeynep Şanlı, Mehmet Kunt, Tuncay Köroğlu. IMPROVED HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS VIA KATUGAMPOLA FRACTIONAL INTEGRALS. SIGMA [Internet]. 2019 Jun. 1;37(2):461-74. Available from: https://izlik.org/JA66CN73PA