Dragomir, Sever S ORCID: 0000-0003-2902-6805 (2021) Error bounds related to midpoint and trapezoid rules for the monotonic integral transform of positive operators in Hilbert spaces. Mathematica Pannonica, 27_NS1 (2). ISSN 0865-2090

Abstract

For a continuous and positive function w(λ), λ 0 and μ a positive measure on (0, ∞) we consider the following monotonic integral transform where the integral is assumed to exist for T a positive operator on a complex Hilbert space H. We show among others that, if β ≥ A, B ≥ α 0, and 0 δ ≤ (B − A)2 ≤ Δ for some constants α, β, δ, Δ, then and where is the second derivative of as a real function. Applications for power function and logarithm are also provided.

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