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On some new fractional Hermite-Hadamard type inequalities for convex and co-ordinated convex functions

Huseyin Budak|Muhammad Aamir Ali|Sadia Sakhi
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2020.12|한국수학논문집 (Korean Journal of Mathematics)|제28권 제4호|pp. 955-971

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키워드

Hermite-Hadamard inequalityConvex functionsfractional integralsco-ordinated convex functions.
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초록

In this study, some new inequalities of Hermite-Hadamard type for convex and co-ordinated convex functions via Riemann-Liouville fractional integrals are derived. It is also shown that the results obtained in this paper are the extension of some earlier ones.

Abstract

In this study, some new inequalities of Hermite-Hadamard type for convex and co-ordinated convex functions via Riemann-Liouville fractional integrals are derived. It is also shown that the results obtained in this paper are the extension of some earlier ones.

참고문헌 (18)

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  2. M. A. Ali, "Some new Simpson’s type inequalities for co-ordinated convex functions in quantum calculus", Mathematical Methods in the Applied Sciences[DOI]
  3. M. A. Ali, "Quantum Hermite-Hadamard type inequalities for functions whose second q b -derivatives absolute value are convex", Advances in Difference Equation (2020)
  4. H. Budak, "Some trapezoid and midpoint type inequalities for newly defined quantum integrals", Proyecciones Journal of Mathematics
  5. H. Budak, "Simpson and Newton type inequalities for convex functions via newly defined quantum integrals", Mathematical Methods in the Applied Sciences (2020)
  6. H. Budak, "Some New Quantum Hermite–Hadamard-Like Inequalities for Coordinated Convex Functions", Journal of Optimization Theory and Applications, pp.1~12 (2020)
  7. H. Budak, "Quantum Ostrowski type integral inequalities for functions of two variables", Mathematical Methods in the Applied Sciences (2020)
  8. F. Chen, "A note on the Hermite-Hadamard inequality for convex functions on the co-ordinates", Journal of Mathematical Inequalities, 8(4), pp.915~923 (2014)
  9. S. S. Dragomir, "Selected Topics on Hermite-Hadamard Inequalities and Applications", RGMIA Monographs, Victoria University, ~ (2000)
  10. A. E. Farissi, "Hadamard-Type Inequalities for Twice Differentiable Functions", RGMIA Research Report collection, 12(1) (2009)
  11. A. E. Farissi, "Simple proof and refinements of Hermite-Hadamard inequality", Journal of Mathematical Inequalities, 4(3), pp.365~369 (2010)
  12. R. Gorenflo, "Fractional Calculus, Integral and Differential Equations of Fractional Order", pp.223~276 (1997), Springer Verlag
  13. A. Kashuri, "New inequalities for generalized m-convex functions via generalized fractional integral operators and their applications", International Journal of Nonlinear Analysis and Applications, 10(2), pp.275~299 (2019)
  14. A. Kashuri, "Fractional integral inequalities for generalized convexity", Tbilisi Mathematical Journal, 13(3), pp.63~83 (2020)
  15. M. E. Ozdemir, "On some new Hadamard-type inequalities for co-ordinated quasi-convex functions", Hacettepe Journal of Mathematics and Statistics, 41(5), pp.697~707 (2012)
  16. J. E. Peˇcari´c, "Convex Functions, Partial Orderings and Statistical Applications" (1992), Academic Press
  17. M. Z. Sarikaya, "On the Hermite-Hadamard-type inequalities for co-ordinated convex functions via fractional integrals", Integral Transforms and Special Functions, 25(2), pp.134~147 (2014)
  18. M. Z. Sarikaya, "Hermite-Hadamard’s inequalities for fractional integrals and related inequalities", Mathematical and Computer Modelling, 57, 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 제2호Hermite-Hadamard-Fejer Type Inequalities for Harmonically Quasi-convex Functions via Fractional IntegralsImdat Iscan, Mehmet Kunt경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제3호Fractional integral inequalities for harmonic geometrically h-convex functionsKhalida Inayat Noor, Muhammad Aslam Noor, SABAH IFTIKHAR장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제3호GENERALIZATION OF INEQUALITIES ANALOGOUS TO HERMITE–HADAMARD INEQUALITY VIA FRACTIONAL INTEGRALSKiran Nazeer, Muhammad Iqbal, Muhammad Iqbal Bhatti대한수학회 · 대한수학회보2015 · 제52권 제3호Fractional integral inequalities of Hermite-Hadamard type for m-HH convex functions with applicationsHui Zhou, Imdat Iscan, Wen Wang장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제3호Riemann-Liouville fractional versions of Hadamard inequality for strongly $(\alpha,m)$-convex functionsGhulam Farid, Lakshmi Narayan Mishra, Laxmi Rathour, Saira Bano Akbar강원경기수학회 · 한국수학논문집2021 · 제29권 제4호

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