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Quadratic Operators and Quadratic Functional Equation

In: Nonlinear Analysis

Author

Listed:
  • M. Adam

    (Higher School of Labour Safety Management in Katowice)

  • S. Czerwik

    (Silesian University of Technology)

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.

Suggested Citation

  • M. Adam & S. Czerwik, 2012. "Quadratic Operators and Quadratic Functional Equation," Springer Optimization and Its Applications, in: Panos M. Pardalos & Pando G. Georgiev & Hari M. Srivastava (ed.), Nonlinear Analysis, edition 127, chapter 0, pages 13-37, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-3498-6_2
    DOI: 10.1007/978-1-4614-3498-6_2
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