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Quadratic Operators and Quadratic Functional Equation

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Nonlinear Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 68))

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Abstract

In the first part of this paper, we consider some quadratic difference operators (e.g., Lobaczewski difference operators) and quadratic-linear difference operators (d’Alembert difference operators and quadratic difference operators) in some special function spaces X λ . We present results about boundedness and find the norms of such operators. We also present new results about the quadratic functional equation. The second part is devoted to the so-called double quadratic difference property in the class of differentiable functions. As an application we prove the stability result in the sense of Ulam–Hyers–Rassias for the quadratic functional equation in a special class of differentiable functions.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Informatics, Higher School of Labour Safety Management in Katowice, Bankowa 8, 40-007, Katowice, Poland

    M. Adam

  2. Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100, Gliwice, Poland

    S. Czerwik

Authors
  1. M. Adam
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  2. S. Czerwik
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Corresponding author

Correspondence to S. Czerwik .

Editor information

Editors and Affiliations

  1. , Department of Industrial & Systems Engin, University of Florida, Weil Hall 401, Gainesville, 32611, Florida, USA

    Panos M. Pardalos

  2. Center for Applied Optimization, Dept. Industrial & Systems, University of Florida, Weil Hall 303, Gainesville, 32611-6595, Florida, USA

    Pando G. Georgiev

  3. , Department of Mathematics & Statistics, University of Victoria, Finnerty Road 3800, Victoria, V8W 3R4, British Columbia, Canada

    Hari M. Srivastava

Additional information

Dedicated to Professor Themistocles M. Rassias on the occasion of his 60th birthday.

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Adam, M., Czerwik, S. (2012). Quadratic Operators and Quadratic Functional Equation. In: Pardalos, P., Georgiev, P., Srivastava, H. (eds) Nonlinear Analysis. Springer Optimization and Its Applications, vol 68. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3498-6_2

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