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Generalized Steffensen’s Inequality by Fink’s Identity

Author

Listed:
  • Asfand Fahad

    (Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari 61100, Pakistan)

  • Saad Ihsan Butt

    (Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan)

  • Josip Pečarić

    (RUDN University, Miklukho-Maklaya str. 6, 117198 Moscow, Russia)

Abstract

By using Fink’s Identity, Green functions, and Montgomery identities we prove some identities related to Steffensen’s inequality. Under the assumptions of n -convexity and n -concavity, we give new generalizations of Steffensen’s inequality and its reverse. Generalizations of some inequalities (and their reverse), which are related to Hardy-type inequality. New bounds of Gr u ¨ ss and Ostrowski-type inequalities have been proved. Moreover, we formulate generalized Steffensen’s-type linear functionals and prove their monotonicity for the generalized class of ( n + 1 ) -convex functions at a point. At the end, we present some applications of our study to the theory of exponentially convex functions.

Suggested Citation

  • Asfand Fahad & Saad Ihsan Butt & Josip Pečarić, 2019. "Generalized Steffensen’s Inequality by Fink’s Identity," Mathematics, MDPI, vol. 7(4), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:329-:d:220057
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