Quadratic Operators and Quadratic Functional Equation

M. Adam () and S. Czerwik ()
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M. Adam: Higher School of Labour Safety Management in Katowice
S. Czerwik: Silesian University of Technology

Chapter Chapter 2 in Nonlinear Analysis, 2012, pp 13-37 from Springer

Abstract: 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.

Keywords: Quadratic; d’Alembert; and Lobaczewski difference operators; X λ spaces; Quadratic functional equation; Stability; 39B52; 39B82; 47H30 (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-3498-6_2

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DOI: 10.1007/978-1-4614-3498-6_2

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