Research Article

Katugampola Fractional Integrals within the Class of Convex Functions

Volume: 3 Number: 1 December 31, 2018
EN

Katugampola Fractional Integrals within the Class of Convex Functions

Abstract

The aim of this paper is to the Hermite-Hadamard type inequalities for functions whose first derivatives in absolute value is s-convex through the instrument of generalized Katugampola fractional integrals.

Keywords

References

  1. W.W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math. 23(1978), 13-20.
  2. F. Chen, A note on the Hermite-Hadamard inequality for convex functions on the coordinates, J. of Math. Inequalities, 8(4), (2014) 915-923.
  3. 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.
  4. G. Cristescua, Boundaries of Katugampola fractional integrals within the class of convex functions, https://www.researchgate.net/publication/313161140.
  5. A. Erdélyi, On fractional integration and its application to the theory of Hankel transforms, The Quarterly Journal of Mathematics, Oxford, Second Series, 11(1940), 293-303.
  6. R. Gorenflo and F. Mainardi, Fractinal calculus: integral and differential equations of fractional order, Springer Verlag, Wien (1997), 223-276.
  7. J. Hadamard, Etude sur les proprietes des fonctions entieres et en particulier d’une fonction considree par, Riemann, J. Math. Pures. et Appl. 58 (1893), 171-215.
  8. H. Hudzik and L. Maligranda, Some remarks on convex functions, Acquationes Math. 48 (1994), 100-111.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Publication Date

December 31, 2018

Submission Date

November 23, 2018

Acceptance Date

December 27, 2018

Published in Issue

Year 2018 Volume: 3 Number: 1

APA
Yaldız, H., & Akdemir, A. O. (2018). Katugampola Fractional Integrals within the Class of Convex Functions. Turkish Journal of Science, 3(1), 40-50. https://izlik.org/JA96PN59LF
AMA
1.Yaldız H, Akdemir AO. Katugampola Fractional Integrals within the Class of Convex Functions. TJOS. 2018;3(1):40-50. https://izlik.org/JA96PN59LF
Chicago
Yaldız, Hatice, and Ahmet Ocak Akdemir. 2018. “Katugampola Fractional Integrals Within the Class of Convex Functions”. Turkish Journal of Science 3 (1): 40-50. https://izlik.org/JA96PN59LF.
EndNote
Yaldız H, Akdemir AO (December 1, 2018) Katugampola Fractional Integrals within the Class of Convex Functions. Turkish Journal of Science 3 1 40–50.
IEEE
[1]H. Yaldız and A. O. Akdemir, “Katugampola Fractional Integrals within the Class of Convex Functions”, TJOS, vol. 3, no. 1, pp. 40–50, Dec. 2018, [Online]. Available: https://izlik.org/JA96PN59LF
ISNAD
Yaldız, Hatice - Akdemir, Ahmet Ocak. “Katugampola Fractional Integrals Within the Class of Convex Functions”. Turkish Journal of Science 3/1 (December 1, 2018): 40-50. https://izlik.org/JA96PN59LF.
JAMA
1.Yaldız H, Akdemir AO. Katugampola Fractional Integrals within the Class of Convex Functions. TJOS. 2018;3:40–50.
MLA
Yaldız, Hatice, and Ahmet Ocak Akdemir. “Katugampola Fractional Integrals Within the Class of Convex Functions”. Turkish Journal of Science, vol. 3, no. 1, Dec. 2018, pp. 40-50, https://izlik.org/JA96PN59LF.
Vancouver
1.Hatice Yaldız, Ahmet Ocak Akdemir. Katugampola Fractional Integrals within the Class of Convex Functions. TJOS [Internet]. 2018 Dec. 1;3(1):40-5. Available from: https://izlik.org/JA96PN59LF