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Journals / Turkish Journal of Science / 2016 / Cilt: 1 - Sayı: 1

Hermite-Hadamard type inequalities for s-convex and s-concave functions via fractional integrals

M. Emin ÖZDEMİR
Merve AVCI-ARDIÇ
Havva KAVURMACI-ÖNALAN
Pages
28–40
Publication Date
2016-12-31
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Comput., 217 (2011) 5171-5176].

📌 3 Key Takeaways

🎯
Objective & Hypothesis:New identity for fractional integrals have been defined.
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Key Findings & Data:It has been determined that the results are related to the results of Avcı et al., proved in [4, published in Appl.
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Conclusion & Impact:Comput., 217 (2011) 5171-5176].
🔬Design:Research Article
📍Scope:2011 Verileri
⚙️Variables:s-convex function · Hölder inequality · Power-mean inequality

Abstract

New identity for fractional integrals have been defined. By using this identity, some new Hermite-Hadamard type inequalities for Riemann-Liouville fractional integral have been developed. It has been determined that the results are related to the results of Avcı et al., proved in [4, published in Appl. Math. Comput., 217 (2011) 5171-5176].

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Cite This Article

ÖZDEMİR, M. E., AVCI-ARDIÇ, M., KAVURMACI-ÖNALAN, H. (2016). Hermite-Hadamard type inequalities for s-convex and s-concave functions via fractional integrals. Turkish Journal of Science, Cilt: 1 - Sayı: 1, 28–40. https://ajindex.com/articles/809528

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References (5)

  1. R. Gorenflo, F. Mainardi, Fractional calculus: integral and differential equations of fractional order, Springer Verlag, Wien (1997), 223-276.
  2. S. Miller and B. Ross, An introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, USA, 1993, p.2. I. Podlubni, Fractional Differential Equations, Academic Press, San Diego, 1999.
  3. M. Avcı, H. Kavurmacı and M.E. Özdemir, New inequalities of Hermite-Hadamard type via convex functions in the second sense with applications, Appl. Math. Comput., 217 (2011) 5171–5176.
  4. H. Kavurmacı, M. Avcı and M.E. Özdemir, New inequalities of hermite-hadamard type for convex functions with applications, JIA, 2011, 2011:86. H. Hudzik, L. Maligranda, Some remarks on s-convex functions, Aequationes Math. 48 (1994) 100–111.
  5. S.S. Dragomir, S. Fitzpatrick, The Hadamard’s inequality for s-convex functions in the second sense, Demonstratio Math. 32 (4) (1999) 687–696.