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Additive p-functional Equations in β-homogeneous F-spaces

심은화
한국수학교육학회|2017.11|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제24권 제4호|pp. 243-251|DOI https://doi.org/10.7468/jksmeb.2017.24.4.243

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참고문헌

키워드

Hyers-Ulam stability¯-homogeneous F-spaceadditive ½-functional equation.
주제분류수학

초록

In this paper, we solve the additive ½-functional equations f(x + y) + f(x ¡ y) ¡ 2f(x) = ½ ³ 2f ³x + y 2 ´ + f(x ¡ y) ¡ 2f(x) ´ (0.1) ; and 2f ³x + y 2 ´ (0.2) + f(x ¡ y) ¡ 2f(x) = ½(f(x + y) + f(x ¡ y) ¡ 2f(x)); where ½ is a ¯xed (complex) number with ½ 6= 1, Using the direct method, we prove the Hyers-Ulam stability of the additive ½- functional equations (0.1) and (0.2) in ¯-homogeneous (complex) F-spaces.

Abstract

In this paper, we solve the additive ½-functional equations f(x + y) + f(x ¡ y) ¡ 2f(x) = ½ ³ 2f ³x + y 2 ´ + f(x ¡ y) ¡ 2f(x) ´ (0.1) ; and 2f ³x + y 2 ´ (0.2) + f(x ¡ y) ¡ 2f(x) = ½(f(x + y) + f(x ¡ y) ¡ 2f(x)); where ½ is a ¯xed (complex) number with ½ 6= 1, Using the direct method, we prove the Hyers-Ulam stability of the additive ½- functional equations (0.1) and (0.2) in ¯-homogeneous (complex) F-spaces.

참고문헌 (25)

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