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Journals / Konuralp Journal of Mathematics / 2026 / Volume: 7 Issue: 1

On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions

Erhan Set
Muhamet Emin Özdemir
Necla Korkut
Pages
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Publication Date
2019-04-15
DOI
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The aim of the present paper is to investigate some new Hermite-Hadamard type integral inequalities for $(\alpha^{*},m)$-convex functions via Riemann-Liouville fractional integrals.

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Objective & Hypothesis:The aim of the present paper is to investigate some new Hermite-Hadamard type integral inequalities for $(\alpha^{*},m)$-convex functions via Riemann-Liouville fractional integrals.
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Key Findings & Data:The aim of the present paper is to investigate some new Hermite-Hadamard type integral inequalities for $(\alpha^{*},m)$-convex functions via Riemann-Liouville fractional integrals.
💡
Conclusion & Impact:The aim of the present paper is to investigate some new Hermite-Hadamard type integral inequalities for $(\alpha^{*},m)$-convex functions via Riemann-Liouville fractional integrals.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fractional Hermite-Hadamard inequalities · $m$-convex function

Abstract

The aim of the present paper is to investigate some new Hermite-Hadamard type integral inequalities for $(\alpha^{*},m)$-convex functions via Riemann-Liouville fractional integrals.

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Cite This Article

Set, E., Özdemir, M. E., Korkut, N. (2019). On New Fractional Hermite-Hadamard Type Inequalities for $(\alpha^{*},m)$-Convex Functions. Konuralp Journal of Mathematics, Volume: 7 Issue: 1. https://ajindex.com/articles/1521736

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References (22)

  1. R. Bai, F. Qi, B. Xi, Hermite-Hadamard type inequalities for the m- and (a;m)-logarithmically convex functions, Filomat, 27 (2013), 1-7.
  2. M.K. Bakula, M.E. Özdemir and J. Pecaric, Hadamard type inequalities for m-convex and (a;m)-convex functions, J.Ineq. Pure Appl. Math., 9(2008), Article 96, [ONL˙INE:http://jipam.vu.edu.au].
  3. S. Belarbi, Z. Dahmani, On some new fractional integral inequalities, J. Ineq. Pure Appl. Math., 10(3) (2009), Art.86.
  4. G. Cristescu, L. Lupsa, Non-connected Convexities abd Applications, Kluwer Academic Publishers, Dordrecht, Holland, (2002).
  5. Z. Dahmani, New inequalities in fractional integrals, Int. J. Nonlinear Sci., 9(4) (2010),493-497.
  6. Z. Gao, M. Li, J. Wang, On some fractional Hermite-Hadamard inequalities via s-convex and s-Godunova-Levin functions and their applications, Bol. Soc. Mat. Mex., DOI 10.1007/s40590-016-0087-9.
  7. E.K. Godunova and V.I. Levin, Neravenstva dlja funckcii sirokogo klassa, soderzascego vypuklye, monotonnye inekotorye drugie vidy funkii, Vycislitel. Mat. i. Fiz. Mezvuzov. Sb. Nauc. Trudov, MGPI, Moskova., (1985),138-142.
  8. I. Iscan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe J. Math. Statis., 43(6) (2014),935-942.
  9. A. A. Kilbas, M. H. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B. V, Amsterdam(2006).
  10. V.G. Mihes¸an, A generalization of the convexity, Seminar on Functional Equations, Approx. and Convex., Cluj-Napoca, (Romania) (1993).
  11. S. Miller, B. Ross, An introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley. Soons. USA., (1993),2.
  12. M. A. Noor, K.I. Noor, M.U. Awan, Geometrically relative convex functions, Appl. Math. Infor. Sci., 8(2) (2014),607-616.
  13. M. E. Özdemir, H. Kavurmacı, E. Set, Ostrowski’s type inequalities for (a;m)-convexity functions, Kyungpook Math. J., 50 (2010), 371-378.
  14. M. E. Özdemir, E. Set, M.Z. Sarıkaya, Some new Hadamard type inequalities for co-ortinated m-convex and (a;m)-convex functions, Hacettepe Journal of Mathematics and Statistics 40 (2) (2011), 219 – 229.
  15. M. Z. Sarıkaya, E. Set, H. Yaldız, N. Basak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Math. Comput. Model., 57 (2013),2403-2407.
  16. E. Set, M. E. Özdemir, M.Z. Sarıkaya, Inequalities of Hermite-Hadamard’s type for functions whose second derivatives absolute values are m-convex, AIP Conference Proceedings, 1309(1) (2010),861-873.
  17. G. Toader, Some generalizations of the convexity, Proceedings of The Colloquium On Appraximation and Optimization, Univ. Cluj-Napoca, (1984),329- 338.
  18. S. Varosanec, On h-convexity, J. Math. Anal. Appl., 326 (2007),303-311.
  19. J. Wang, J. Deng, M. Feˇckan, Hermite-Hadamard type inequalities for r-convex functions via Riemann-Liouville fractional integrals, Ukr. Math. J., 65 (2013),193-211.
  20. J. Wang, X. Li, M. Feckan, Y. Zhou, Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals via two kinds of convexity Appl. Anal. Int. J., 92 (2013),2241-2253.
  21. A. A. Kilbas, M. H. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B. V, Amsterdam(2006).
  22. S. Varosanec, On h-convexity, J. Math. Anal. Appl., 326 (2007),303-311.