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On the Hyers-Ulam-Rassias stability of the Jensen equation in distributions

정재영|이은구
대한수학회 (The Korean Mathematical Society)|2011.04|대한수학회논문집 (Communications of the KMS)|제26권 제2호|pp. 261-271

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참고문헌

키워드

stabilitydistributionsGauss transformsheat kerneltempered distributionJensen functional equation
주제분류수학

초록

We consider the Hyers-Ulam-Rassias stability problem ∥2u (기호) A/ 2 -u(기호) P_1 -u(기호) P_2 ∥≤ε (|x|^p +|y|^p), x, y ∈ R^n for the Schwartz distributions u, which is a distributional version of the Hyers-Ulam-Rassias stability problem of the Jensen functional equation (수식)≤ε (|x|^p +|y|^p), x, y ∈ R^n for the function f : R^n → C.

Abstract

We consider the Hyers-Ulam-Rassias stability problem ∥2u (기호) A/ 2 -u(기호) P_1 -u(기호) P_2 ∥≤ε (|x|^p +|y|^p), x, y ∈ R^n for the Schwartz distributions u, which is a distributional version of the Hyers-Ulam-Rassias stability problem of the Jensen functional equation (수식)≤ε (|x|^p +|y|^p), x, y ∈ R^n for the function f : R^n → C.

참고문헌 (24)

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관련 논문AI추천

The stability of the sine and cosine functional equations in Schwartz distributions정재영, Jeongwook Chang대한수학회 · 대한수학회보2009 · 제46권 제1호Hyers-Ulam-Rassias stability of quadratic functional equation in the space of Schwartz tempered distributions정재영한국수학교육학회 · 이론수학과 교직수학2005 · 제12권 제2호On the Hyers-Ulam-Rassias stability of Jensen's equationDongyan Zhang, Jian Wang대한수학회 · 대한수학회보2009 · 제46권 제4호ASYMPTOTIC BEHAVIORS OF JENSEN TYPE FUNCTIONAL EQUATIONS IN HALF PLANES김규태, 김상엽, 박광현, 이기휘, 이재호한국수학교육학회 · 이론수학과 교직수학2011 · 제18권 제2호On the stability of a Cauchy-Jensen functional equation이양희, 전길웅, 조영선대한수학회 · 대한수학회논문집2008 · 제23권 제3호Hyers-Ulam Stability of Jensen Functional Equation in p- Banach Spaces김학만, 손은영, 전길웅경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제3호

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