ON AN L-VERSION OF A PEXIDERIZED QUADRATIC FUNCTIONAL INEQUALITY

• Journal title : Honam Mathematical Journal
• Volume 33, Issue 1,  2011, pp.73-84
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2011.33.1.073
Title & Authors
ON AN L-VERSION OF A PEXIDERIZED QUADRATIC FUNCTIONAL INEQUALITY
Chung, Jae-Young;

Abstract
Let f, g, h, k : $\small{\mathbb{R}^n{\rightarrow}\mathbb{C}}$ be locally integrable functions. We deal with the $\small{L^{\infty}}$-version of the Hyers-Ulam stability of the quadratic functional inequality and the Pexiderized quadratic functional inequality $\small{{\parallel}f(x + y) + f(x - y) -2f(x) - 2f(y){\parallel}_{L^{\infty}(\mathbb{R}^n)}\leq\varepsilon}$ $\small{{\parallel}f(x + y) + g(x - y) -2h(x) - 2f(y){\parallel}_{L^{\infty}(\mathbb{R}^n)}\leq\varepsilon}$ based on the concept of linear functionals on the space of smooth functions with compact support.
Keywords
quadratic functional equation;stability;locally integrable functions;heat kernel;almost everywhere sense;
Language
English
Cited by
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