On the Stability of an Additive and Quadratic Functional Equation

Choonkil Park ()
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Choonkil Park: Hanyang University

Chapter Chapter 34 in Nonlinear Analysis, 2012, pp 539-549 from Springer

Abstract: Abstract In Park et al. (J. Chungcheong Math. Soc. 21:455–466, 2008) considered the following Jensen additive and quadratic type functional equation $$2 f \biggl(\frac{x+y}{2} \biggr) + f \biggl( \frac{x-y}{2} \biggr ) + f \biggl(\frac{y-x}{2} \biggr) = f(x) + f(y) . $$ In this paper, we investigate the following additive and quadratic functional equation 34.1 $$ 2 f(x+y) + f(x-y) + f(y-x) = 3f(x) + f(-x) + 3f(y) + f(-y) . $$ Furthermore, we prove the generalized Hyers–Ulam stability of the functional equation (34.1) in Banach spaces.

Keywords: Additive and quadratic type functional equation; Additive mapping; Quadratic mapping; Generalized Hyers–Ulam stability; 39B72; 46C05 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-3498-6_34

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