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Generalised Trapezoid-Type Inequalities for Complex Functions Defined on Unit Circle with Applications for Unitary Operators in Hilbert Spaces

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Abstract

Some generalised trapezoid-type inequalities for the Riemann–Stieltjes integral of continuous complex valued integrands defined on the complex unit circle \({\mathcal{C}(0, 1)}\) and various subclasses of integrators of bounded variation are given. Natural applications for functions of unitary operators in Hilbert spaces are provided.

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Authors and Affiliations

  1. Mathematics, College of Engineering and Science, Victoria University, PO Box 14428, Melbourne City, MC, 8001, Australia

    S. S. Dragomir

  2. School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg, 2050, South Africa

    S. S. Dragomir

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  1. S. S. Dragomir
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Correspondence to S. S. Dragomir.

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Dragomir, S.S. Generalised Trapezoid-Type Inequalities for Complex Functions Defined on Unit Circle with Applications for Unitary Operators in Hilbert Spaces. Mediterr. J. Math. 12, 573–591 (2015). https://doi.org/10.1007/s00009-014-0434-x

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  • DOI: https://doi.org/10.1007/s00009-014-0434-x

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