Results in Mathematics

, 74:53 | Cite as

Functionals Related to Gauss–Pólya Type Inequalities Involving Derivatives

  • Sanja VarošanecEmail author


We consider several functionals associated with inequalities which involve derivatives of functions. As a consequence of those results we get new refinements and improvements for the Gauss–Pólya inequalities.


Derivative functional the Gauss–Pólya inequalities Hölder type inequality Minkowski type inequality monotonicity superadditivity 

Mathematics Subject Classification

39B62 26D15 26D10 



  1. 1.
    Beesack, P.R.: Inequalities for absolute moments of a distribution: from Laplace to Von Mises. J. Math. Anal. Appl. 98, 435–457 (1984)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Mitrinović, D.S., Pečarić, J.E., Fink, A.M.: Classical and New Inequalities in Analysis. Kluwer Academic Publishers, Dordrecht (1993)CrossRefGoogle Scholar
  3. 3.
    Pečarić, J., Varošanec, S.: A generalization of Pólya’s inequalities. In: Agarwal, R.P. (ed.) Inequalities and Applications. WSSIAA 3, pp. 501–504. World Scientific Publishing Company, Singapore (1994)CrossRefGoogle Scholar
  4. 4.
    Pólya, G., Szegö, G.: Aufgaben und Lehrsätze aus der Analysis, I, II. Springer, Berlin (1925)zbMATHGoogle Scholar
  5. 5.
    Varošanec, S.: Inequalities of Minkowski’s type. Real Anal. Exch. 20(1), 250–255 (1994–1995)Google Scholar
  6. 6.
    Varošanec, S., Pečarić, J.: Some integral inequalities with application for bounds for moments of a distribution. J. Aust. Math. Soc. Ser. B Appl. Math. 38, 325–335 (1997)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceUniversity of ZagrebZagrebCroatia

Personalised recommendations