Rad HAZU, Matematičke znanosti, Vol. 22 (2018), 63-75.

HERMITE-HADAMARD TYPE INEQUALITIES FOR GENERALIZED (s,m,φ)-PREINVEX GODUNOVA-LEVIN FUNCTIONS

Artion Kashuri and Rozana Liko

Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali", Vlora, Albania
e-mail: artionkashuri@gmail.com

Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali", Vlora, Albania
e-mail: rozanaliko86@gmail.com


Abstract.   In the present paper, a new class of generalized (s,m,φ)-preinvex Godunova-Levin function of the second kind is introduced. Moreover, some left inequalities of Gauss-Jacobi type quadrature formula are given and some Hermite-Hadamard type inequalities for generalized (s,m,φ)-preinvex Godunova-Levin functions of the second kind via classical integrals are established. At the end, some applications to special means are given.

2010 Mathematics Subject Classification.   26A51, 26A33, 26D07, 26D10, 26D15.

Key words and phrases.   (s,m)-Godunova-Levin function, Hölder’s inequality, power mean inequality, m-invex, P-function.


Full text (PDF) (free access)

DOI: http://doi.org/10.21857/m16wjc6rl9


References:

  1. P. S. Bullen, Handbook of Means and Their Inequalities, Kluwer Academic Publishers, Dordrecht, 2003.
    MathSciNet     CrossRef

  2. S. S. Dragomir, Inequalities of Hermite-Hadamard type for h-convex functions on linear spaces, Proyecciones 34 (2015), 323-341.
    MathSciNet     CrossRef

  3. S. S. Dragomir, n-points inequalities of Hermite-Hadamard type for h-convex functions on linear spaces, Armen. J. Math. 8 (2016), 38-57.
    MathSciNet

  4. S. S. Dragomir, J. Pečarić and L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math. 21 (1995), 335–341.
    MathSciNet

  5. T. S. Du, J. G. Liao and Y. J. Li, Properties and integral inequalities of Hadamard- Simpson type for the generalized (s,m)-preinvex functions, J. Nonlinear Sci. Appl. 9 (2016), 3112–3126.
    MathSciNet     CrossRef

  6. E. K. Godunova and V. I. Levin, Inequalities for functions of a broad class that contains convex, monotone and some other forms of functions, Numer. Math. Math. Phys. 166 (1985), 138–142.
    MathSciNet

  7. E. K. Godunova and V. I. Levin, Neravenstva dlja funkcii sirokogo klassa, soderzascego vypuklye, monotonnye i nekotorye drugie vidy funkii, Vycislitel. Mat. i. Fiz. Mezvuzov. Sb. Nauc. Trudov, MGPI, Moskva. 9 (1985), 138-142.

  8. H. Kavurmaci, M. Avci and M. E. Özdemir, New inequalities of Hermite-Hadamard type for convex functions with applications, arXiv:1006.1593v1 [math. CA], 2010.

  9. W. Liu, New integral inequalities involving beta function via P-convexity, Miskolc Math. Notes 15 (2014), 585–591.
    MathSciNet

  10. W. Liu, W. Wen and J. Park, Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals, J. Nonlinear Sci. Appl. 9 (2016), 766–777.
    MathSciNet     CrossRef

  11. D. S. Mitrinović and J. Pečarić, Note on a class of functions of Godunova and Levin, C. R. Math. Rep. Acad. Sci. Can. 12 (1990), 33–36.
    MathSciNet

  12. D. S. Mitrinović, J. Pečarić and A. M. Fink, Classical and new inequalities in analysis, Kluwer Academic, Dordrecht, 1993.
    MathSciNet     CrossRef

  13. M. A. Noor, K. I. Noor and M. U. Awan, Fractional Ostrowski inequalities for (s,m)-Godunova-Levin functions, Facta Univ. Ser. Math. Inform. 30 (2015), 489–499.
    MathSciNet

  14. M. E. Özdemir, E. Set and M. Alomari, Integral inequalities via several kinds of convexity, Creat. Math. Inform. 20 (2011), 62–73.
    MathSciNet

  15. D. D. Stancu, G. Coman and P. Blaga, Analiza numerica si teoria aproximarii, Cluj-Napoca: Presa Universitara Clujeana, 2, 2002.
    MathSciNet


Rad HAZU Home Page