Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0951.39008
Rassias, John Michael
Solution of the Ulam stability problem for quartic mappings. (English)
[J] Glas. Mat., III. Ser. 34, No.2, 243-252 (1999). ISSN 0017-095X

The author studies the Hyers-Ulam stability of the functional equation $$f(x+2y) + f(x-2y) + 6 f(x) = 4 \left [ f(x+y) + f(x-y) + 6 f(y) \right ]\tag FE$$ using the so called direct method of Hyers. A function $F$ is called a quartic mapping if it satisfies the above functional equation (FE). The author proves the following result: Let $X$ be a normed linear space and $Y$ be a real complete normed linear space. If $f: X \to Y$ satisfies the inequality $$\|f(x+2y) + f(x-2y) + 6 f(x) - 4 \left [ f(x+y) + f(x-y) + 6 f(y) \right ] \|\leq \varepsilon \tag FI$$ for all $x, y \in X$ with a constant $\varepsilon \geq 0$ (independent of $x$ and $y$), then there exists a unique quartic function $F : X \to Y$ such that $\|F(x) - f(x) \|\leq {{17} \over {180}} \varepsilon $. This result is obtained through six lemmas.
[Prasanna Sahoo (Louisville)]

MSC 2000:: *39B82 Stability, separation, extension, and related topics
39B62 Systems of functional equations
39B52 Functional equations for functions with more general domains

Keywords: functional equation; quartic map; functional inequality; Hyers-Ulam stability; direct method; normed linear space

Cited in: Zbl 1237.39026

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]