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Journals / Turkish Journal of Science / 2018 / Cilt: 3 - Sayı: 1

Katugampola Fractional Integrals within the Class of Convex Functions

Hatice YALDIZ
Ahmet Ocak AKDEMİR
Pages
40–50
Publication Date
2018-12-31
DOI
—
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⚡ TL;DR(Too Long; Didn't Read)

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.

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Objective & Hypothesis: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.
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Key Findings & Data: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.
💡
Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:s-convex function · Hermite-Hadamard type inequalities · Katugampola fractional integrals

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.

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Cite This Article

YALDIZ, H., AKDEMİR, A. O. (2018). Katugampola Fractional Integrals within the Class of Convex Functions. Turkish Journal of Science, Cilt: 3 - Sayı: 1, 40–50. https://ajindex.com/articles/809521

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References (13)

  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. 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.
  5. R. Gorenflo and F. Mainardi, Fractinal calculus: integral and differential equations of fractional order, Springer Verlag, Wien (1997), 223-276.
  6. 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.
  7. H. Hudzik and L. Maligranda, Some remarks on convex functions, Acquationes Math. 48 (1994), 100-111.
  8. U. N. Katugampola, New approach to a generalized fractional integrals, Appl. Math. Comput., 218 (4) (2011), 860-865.
  9. U. N. Katugampola, New approach to a generalized fractional derivatives, Bull. Math. Anal. Appl., Volume 6 Issue 4 (2014), Pages 1-15.
  10. A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, 204, Elsevier Sci. B.V., Amsterdam, 2006.
  11. H. Kober, On fractional integrals and derivatives, The Quarterly J. Math. ( Oxford Series), 11 (1) (1940), 193-211.
  12. S. Miller and B. Ross, An introduction to the fractional calculusand fractional differential equations, John Wiley & Sons, USA, 1993, p.2. M. Z. Sarıkaya, E. Set, H. Yaldiz, N. Ba ak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Math Comput Model. 2013;57(9-10):2403-2407.
  13. M. Z. Sarıkaya and H. Yildirim, On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals, Miskolc Mathematical Notes, Vol. 17 (2016), No. 2, pp. 1049-1059.