Popoviciu and Čebyšev-Popoviciu Type Identities and Inequalities

Nazia Irshad, Asif R. Khan, Faraz Mehmood and Josip Pečarić
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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

Chapter Chapter 4 in New Perspectives on the Theory of Inequalities for Integral and Sum, 2021, pp 213-298 from Springer

Abstract: 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.

Date: 2021
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DOI: 10.1007/978-3-030-90563-7_4

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