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Journals / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2019 / Cilt: 9 - Sayı: 1

Fractional Hermite-Hadamard type inequalities for functions whose derivatives are extended s-(α, m)-preinvex

Badreddine MEFTAH
Abdourazek SOUAHI
Pages
73–81
Publication Date
2022-10-11
DOI
—
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AI Summary & Key Takeaways

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

In this paper, we introduce the class of extended s-(α, m)-preinvex functions.We establish a new fractional integral identity and derive some new fractionalHermite-Hadamard type inequalities for functions whose derivatives are in thisnovel class of function.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce the class of extended s-(α, m)-preinvex functions.We establish a new fractional integral identity and derive some new fractionalHermite-Hadamard type inequalities for functions whose derivatives are in thisnovel class of function.
📊
Key Findings & Data:In this paper, we introduce the class of extended s-(α, m)-preinvex functions.We establish a new fractional integral identity and derive some new fractionalHermite-Hadamard type inequalities for functions whose derivatives are in thisnovel class of function.
💡
Conclusion & Impact:In this paper, we introduce the class of extended s-(α, m)-preinvex functions.We establish a new fractional integral identity and derive some new fractionalHermite-Hadamard type inequalities for functions whose derivatives are in thisnovel class of function.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we introduce the class of extended s-(α, m)-preinvex functions.We establish a new fractional integral identity and derive some new fractionalHermite-Hadamard type inequalities for functions whose derivatives are in thisnovel class of function.

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Cite This Article

MEFTAH, B., SOUAHI, A. (2022). Fractional Hermite-Hadamard type inequalities for functions whose derivatives are extended s-(α, m)-preinvex. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 9 - Sayı: 1, 73–81. https://ajindex.com/articles/440603

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References (9)

  1. Mitrinović, D.S., Pečarić, J.E. and Fink, A.M. (1993). Classical and new inequalities in anal- ysis. Mathematics and its Applications (East European Series), 61. Kluwer Academic Pub- lishers Group, Dordrecht. Khan, M.A., Khurshid, Y., Ali, T. and Rehman, N. (2018). Inequalities for Hermite- Hadamard type with applications, Punjab Univ. J. Math. (Lahore), 50(3), 1–12.
  2. Chu, Y.M., Khan, M.A., Khan, T.U. and Ali, T. (2016). Generalizations of Hermite- Hadamard type inequalities for MT-convex functions, J. Nonlinear Sci. Appl. 9(6), 4305– 4316. Set, E., Karataş, S.S. and Khan, M.A. (2016). Hermite-Hadamard type inequalities obtained via fractional integral for differen- tiable m-convex and (α, m)-convex functions, Int. J. Anal. 2016, Art. ID 4765691, 8 pp. Chu, Y.M., Khan, M.A., Ali, T. and Dragomir, S.S. (2017). Inequalities for α- fractional differentiable functions, J. Inequal. Appl. 2017, Paper No. 93, 12 pp. Khan, M.A., Ali, T. and Dragomir, S.S. (2018). Hermite–Hadamard type inequalities for conformable fractional integrals, Rev. R. Acad. Cienc. Exactas Fı́s. Nat. Ser. A Math. RACSAM, 112(4), 1033–1048.
  3. Khan, M.A., Khurshid, Y. and Ali, T. (2017). Hermite-Hadamard inequality for fractional integrals via η-convex functions, Acta Math. Univ. Comenian. (N.S.), 86(1), 153–164.
  4. Khan, M.A., Chu, Y.M., Khan, T.U. and Khan, J. (2017). Some new inequalities of Hermite-Hadamard type for s-convex func- tions with applications, Open Math., 15, 1414–1430.
  5. Khan, M.A., Khurshid, Y., Ali, T. and Rehman, N. (2016). Inequalities for three times differentiable functions, Punjab Univ. J. Math. (Lahore), 46(2), 35–48.
  6. Kirmaci, U.S. and Özdemir, M.E. (2004). Some inequalities for mappings whose deriva- tives are bounded and applications to special means of real numbers. Appl. Math. Lett., 17(6), 641–645.
  7. Sarikaya, M.Z., Set, E., Yaldiz, H. and Başak, N. (2013). Hermite–Hadamard’s in- equalities for fractional integrals and re- lated fractional inequalities. Mathematical and Computer Modelling. 57(9), 2403-2407.
  8. Zhu, C., Fečkan, M. and Wang, J. (2012). Fractional integral inequalities for differen- tiable convex mappings and applications to special means and a midpoint formula. J. Appl. Math. Stat. Inf. 8(2), 21-28. Pečarić, J.E., Proschan, F. and Tong, Y.L. (1992). Convex functions, partial orderings, and statistical applications. Mathematics in Science and Engineering. 187. Academic Press,
  9. Inc., Boston, MA. Dragomir, S.S., Pečarić, J.E. and Persson, L.E. (1995). Some inequali