Abstract

DRAGOMIR, Silvestru Sever. On some Chebyshev type inequalities for the complex integral. Integración - UIS [online]. 2019, vol.37, n.2, pp.307-317.  Epub Oct 10, 2019. ISSN 0120-419X.  https://doi.org/10.18273/revint.v37n2-2019006.

Assume that f and g are continuous on γ, γ ⊂ ℂ is a piecewise smooth path parametrized by z (t) ,t ∈ [a, b] from z (a) = u to z (b) = w with w ≠ u, and the complex Chebyshev functional is defined by

In this paper we establish some bounds for the magnitude of the functional D γ (f, g) under Lipschitzian assumptions for the functions f and g, and provide a complex version for the well known Chebyshev inequality.

MSC2010: 26D15, 26D10, 30A10, 30A86.

Keywords : Complex integral; Continuous functions; Holomorphic functions; Chebyshev inequality.

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