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GENERALIZATION OF INEQUALITIES ANALOGOUS TO HERMITE–HADAMARD INEQUALITY VIA FRACTIONAL INTEGRALS

Muhammad Iqbal|Muhammad Iqbal Bhatti|Kiran Nazeer
대한수학회 (The Korean Mathematical Society)|2015.05|대한수학회보 (Bulletin of the KMS)|제52권 제3호|pp. 707-716

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참고문헌

키워드

convex functionsHermite–Hadamard’s inequalitypower-mean inequalityRiemann-Liouville fractional integration
주제분류수학

초록

Some Hermite–Hadamard type inequalities for the fractional integrals are established and these results have some relationship with the obtained results of [11, 12].

Abstract

Some Hermite–Hadamard type inequalities for the fractional integrals are established and these results have some relationship with the obtained results of [11, 12].

참고문헌 (14)

  1. G. Anastassiou, "Mont-gomery identities for fractional integrals and related fractional inequalities", J. Inequal. Pure Appl. Math, 10(4), pp.6~ (2009)
  2. S. Belarbi, "On some new fractional integral inequalities", J. Inequal. Pure Appl. Math, 10(3), pp.5~ (2009)
  3. Z. Dahmani, "New inequalities in fractional integrals", Int. J. Nonlinear Sci, 9(4), pp.493~497 (2010)
  4. Z. Dahmani, "On Minkowski and Hermite-Hadamard integral inequalities via fractional inte-gration", Ann. Funct. Anal, 1(1), pp.51~58 (2010)
  5. Z. Dahmani, "New generalisations of Gruss inequality using Riemann-Liouville fractional integrals", Bull. Math. Anal. Appl, 2(3), pp.93~99 (2010)
  6. Z. Dahmani, "Some fractional integral inequalities", Nonl. Sci. Lett. A, 1(2), pp.155~160 (2010)
  7. S. S. Dragomir, "Some new fractional Integral Hermite–Hadamard type inequalities", Journal of Computational Analysis and Application (2015)
  8. Selected topics on Hermite–Hadamard in-equalities and applications, RGMIA Monographs, "S. S. Dragomir", Victoria University, ~ (2000)
  9. R. Gorenflo, "Fractional Calculus: Integral and Differential Equations of Fractional Order, Fractals and fractional calculus in continuum mechanics (Udine, 1996)", CISM Courses and Lectures, 378, pp.223~276 (1997), Springer
  10. S. Hussain, "Hadamard-type inequalities for s-convex func-tions I", Punjab Univ. J. Math, 41, pp.51~60 (2009)
  11. U. S. Kirmaci, "Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula", Appl. Math. Comput, 147(1), pp.137~146 (2004)
  12. U. S. Kirmaci, "On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula", Appl. Math. Comput, 153(2), pp.361~368 (2004)
  13. M. Muddassr, "Some New s-Hermite-Hadamard type for differentiable functions and their applications", Proceeding of the Pakistan Academy of Sciences, 49(1), pp.9~17 (2012)
  14. M. Z. Sarikaya, "Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities", Math. Comput. Model, 57(9-10), pp.2403~2407 (2013)

관련 논문AI추천

FRACTIONAL HERMITE-HADAMARD TYPE INEQUALITIES FOR n-TIMES r-CONVEX FUNCTIONSBADREDDINE MEFTAH, MERIEM MERAD, NAWEL OUANAS장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2018 · 제21권 제2호On some new fractional Hermite-Hadamard type inequalities for convex and co-ordinated convex functionsHuseyin Budak, Muhammad Aamir Ali, Sadia Sakhi강원경기수학회 · 한국수학논문집2020 · 제28권 제4호Fractional integral inequalities of Hermite-Hadamard type for m-HH convex functions with applicationsHui Zhou, Imdat Iscan, Wen Wang장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제3호New Generalizations of Ostrowski-Like Type Inequalities for Fractional IntegralsCetin Yildiz, Mehmet Zeki Sarikaya, Muhamet Emin Ozdemir경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제1호Hermite-Hadamard-Fejer Type Inequalities for Harmonically Quasi-convex Functions via Fractional IntegralsImdat Iscan, Mehmet Kunt경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제3호On Generalizations of the Hadamard Inequality for (α,m)-Convex FunctionsErhan Set, Jamal Rooin, Maryam Sardari, Muhamet Emin Ozdemir경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2012 · 제52권 제3호

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