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On the Hyers-Ulam-Rassias stability of Jensen's equation

Jian Wang|Dongyan Zhang
대한수학회 (The Korean Mathematical Society)|2009.07|대한수학회보 (Bulletin of the KMS)|제46권 제4호|pp. 645-656

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키워드

Hyers-Ulam-Rassias stabilityJensen's functional equation
주제분류수학

초록

J. Wang [21] proposed a problem: whether the Hyers-Ulam- Rassias stability of Jensen’'s equation for the case p, q, r, s ∈(β,1/β)＼{1} holds or not under the assumption that G and E are β-homogeneous F-space (0<β<1). The main purpose of this paper is to give an answer to Wang’'s problem. Furthermore, we proved that the stability property of Jensen’'s equation is not true as long as p or q is equal to β,1/β, or ¯β_(2)/β_(1) (0<β_(1),β_(2)≤1).

Abstract

J. Wang [21] proposed a problem: whether the Hyers-Ulam- Rassias stability of Jensen’'s equation for the case p, q, r, s ∈(β,1/β)＼{1} holds or not under the assumption that G and E are β-homogeneous F-space (0<β<1). The main purpose of this paper is to give an answer to Wang’'s problem. Furthermore, we proved that the stability property of Jensen’'s equation is not true as long as p or q is equal to β,1/β, or ¯β_(2)/β_(1) (0<β_(1),β_(2)≤1).

참고문헌 (25)

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