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On q-Hermite–Hadamard inequalities for general convex functions

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Abstract

The Hermite–Hadamard inequality was first considered for convex functions and has been studied extensively. Recently, many extensions were given with the use of general convex functions. In this paper we present some variants of the Hermite–Hadamard inequality for general convex functions in the context of q-calculus. From our theorems, we deduce some recent results in the topic.

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References

  1. Alp, N., Sarikaya, M.Z., Kunt, M., Iscan, I.: \(q\)-Hermite-Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions. J. King Saud. Univ. Sci. 30, 193–203 (2018)

    Article  Google Scholar 

  2. Bessenyei, M., Páles, Z.: On generalized higher-order convexity and Hermite-Hadamard-type inequalities. Acta Sci. Math. (Szeged) 70, 13–24 (2004)

    MathSciNet  MATH  Google Scholar 

  3. S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite–Hadamard Inequalities, RGMIA Monographs, Victoria University (2000), available at rgmia.vu.edu.au/monographs/hermite_hadamard.html

  4. T. Ernst, A Comprehensive Treatment of \(q\)-Calculus, Birkhäuser/Springer (Basel, 2012)

  5. Jackson, F.H.: On \(q\)-functions and a certain difference operator. Trans. Roy. Soc. Edin. 46, 253–281 (1908)

    Article  Google Scholar 

  6. Jackson, F.H.: On \(q\)-definite integrals. Quart. J. Pure Appl. Math. 41, 193–203 (1910)

    MATH  Google Scholar 

  7. Jhanthanam, S., Tariboon, J., Ntouyas, S.K., Nonlaopon, K.: On \(q\)-Hermite-Hadamard inequalities for differentiable convex functions. Mathematics 7, 632 (2019)

    Article  Google Scholar 

  8. V. Kac and P. Cheung, Quantum Calculus, Springer (New York, 2002)

  9. Klaričić, M., Neuman, E., Pečarić, J., Šimić, V.: Hermite-Hadamard's inequalities for multivariate \(g\)-convex functions. Math. Inequal. Appl. 8, 305–316 (2005)

    MathSciNet  MATH  Google Scholar 

  10. Moslehian, M.S.: Matrix Hermite-Hadamard type inequalities. Houston J. Math. 39, 177–189 (2013)

    MathSciNet  MATH  Google Scholar 

  11. Noor, M.A., Noor, K.I., Awan, M.U.: Hermite-Hadamard inequalities for modified \(h\)-convex functions. Transylv. J. Math. Mech. 6, 171–180 (2014)

    MathSciNet  MATH  Google Scholar 

  12. Noor, M.A., Noor, K.I., Awan, M.U.: A new Hermite-Hadamard type inequality for \(h\)-convex functions. Creat. Math. Inform. 24, 191–197 (2015)

    MathSciNet  MATH  Google Scholar 

  13. Sarikaya, M.Z., Saglam, A., Yildirim, H.: On some Hadamardtype inequalities for \(h\)-convex functions. J. Math. Inequal. 2, 335–341 (2008)

    Article  MathSciNet  Google Scholar 

  14. Tariboon, J., Ntouyas, S.K.: Quantum calculus on finite intervals and applications to impulsive difference equations. Adv. Diff. Equ. 282, 1–19 (2013)

    MathSciNet  MATH  Google Scholar 

  15. Tariboon, J., Ntouyas, S.K.: Quantum integral inequalities on finite intervals. J. Inequal. Appl. 2014, 121 (2014)

    Article  MathSciNet  Google Scholar 

  16. G. Toader, Some generalizations of the convexity, in: Proceedings of the Colloquium on Approximation and Optimization (Cluj-Napoca, 1985), Univ. of Cluj-Napoca (1985), pp. 329–338

  17. Varošanec, S.: On \(h\)-convexity. J. Math. Anal. Appl. 326, 303–311 (2007)

    Article  MathSciNet  Google Scholar 

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Acknowledgement

The authors thank the anonymous referee for useful suggestions to improve the presentation of the results.

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Authors and Affiliations

  1. Department of Economy, Quantitative Methods and Economic History, Pablo de Olavide University, Carretera de Utrera Km. 1, 41013, Sevilla, Spain

    S. Bermudo

  2. Department of Mathematics, Juhász Gyula Faculty of Education, University of Szeged, Hattyas utca 10, 6725, Szeged, Hungary

    P. Kórus

  3. Facultad de Ciencias Exactas y Naturales y Agrimensura, Universidad Nacional del Nordeste, Corrientes Capital, 3400, Argentina

    J. E. Nápoles Valdés

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  1. S. Bermudo
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  2. P. Kórus
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  3. J. E. Nápoles Valdés
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Correspondence to P. Kórus.

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Bermudo, S., Kórus, P. & Nápoles Valdés, J.E. On q-Hermite–Hadamard inequalities for general convex functions. Acta Math. Hungar. 162, 364–374 (2020). https://doi.org/10.1007/s10474-020-01025-6

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  • DOI: https://doi.org/10.1007/s10474-020-01025-6

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