New Upper and Lower Bounds for the Čebyšev Functional

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Cerone, Pietro and Dragomir, Sever S (2002) New Upper and Lower Bounds for the Čebyšev Functional. RGMIA research report collection, 5 (Supp).


New bounds are developed for the Čebyšev functional utilising an identity involving a Riemann-Stieltjes integral. A refinement of the classical Čebyšev inequality is produced for f monotonic non-decreasing, g continuous and M(g; t, b) −M(g; a, t) ≥ 0, for t ∈ [a, b] where M(g; c, d) is the integral mean over [c, d].

Item type Article
Subjects Historical > FOR Classification > 0102 Applied Mathematics
Historical > FOR Classification > 0103 Numerical and Computational Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords Čebyšev functional, bounds, refinement
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