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ASYMPTOTIC BEHAVIORS OF JENSEN TYPE FUNCTIONAL EQUATIONS IN HALF PLANES

이재호|박광현|김규태|김상엽|이기휘
한국수학교육학회|2011.05|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제18권 제2호|pp. 113-128

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참고문헌

키워드

Hyers-Ulam stabilityJensen type functional equationPexider equation.
주제분류수학

초록

Let f : R → C. We consider the Hyers-Ulam stability of Jensen type functional inequality |f(px + qy) − Pf(x) − Qf(y)| ≤ ?in the half planes {(x,y) : kx+sy ≥ d} for fixed d,k,s ∈ R with k ?= 0 or s ?= 0. As consequences of the results we obtain the asymptotic behaviors of f satisfying |f(px + qy) − Pf(x) − Qf(y)| → 0as kx + sy → ∞.

Abstract

Let f : R → C. We consider the Hyers-Ulam stability of Jensen type functional inequality |f(px + qy) − Pf(x) − Qf(y)| ≤ ?in the half planes {(x,y) : kx+sy ≥ d} for fixed d,k,s ∈ R with k ?= 0 or s ?= 0. As consequences of the results we obtain the asymptotic behaviors of f satisfying |f(px + qy) − Pf(x) − Qf(y)| → 0as kx + sy → ∞.

참고문헌 (26)

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