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Popoviciu and Čebyšev-Popoviciu Type Identities and Inequalities

In: New Perspectives on the Theory of Inequalities for Integral and Sum

Author

Listed:
  • Nazia Irshad

    (Dawood University of Engineering and Technology, Department of Mathematics)

  • Asif R. Khan

    (University of Karachi, Department of Mathematics)

  • Faraz Mehmood

    (Dawood University of Engineering and Technology, Department of Mathematics)

  • Josip Pečarić

    (Croatian Academy of Sciences and Arts)

Abstract

The main aim of this section is to extend the definitions of ∇-convex and completely monotonic functions for two variables. We would construct some examples and applications of completely monotonic functions. In present section, some general identities of Popoviciu type for discrete case for sums ∑ i = 1 M ∑ j = 1 N p i j f ( x i , y j ) $$\sum _{i=1}^M\sum _{j=1}^N p_{ij} f(x_i, y_j)$$ and ∑ i = 1 M ∑ j = 1 N p i j a i j $$\sum _{i=1}^M\sum _{j=1}^N p_{ij} a_{ij}$$ have been deduced for function and sequence involving higher order ∇ operator respectively.

Suggested Citation

  • Nazia Irshad & Asif R. Khan & Faraz Mehmood & Josip Pečarić, 2021. "Popoviciu and Čebyšev-Popoviciu Type Identities and Inequalities," Springer Books, in: New Perspectives on the Theory of Inequalities for Integral and Sum, chapter 0, pages 213-298, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-90563-7_4
    DOI: 10.1007/978-3-030-90563-7_4
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