바로가기메뉴

본문 바로가기 주메뉴 바로가기

ACOMS+ 및 학술지 리포지터리 설명회

  • 한국과학기술정보연구원(KISTI) 서울분원 대회의실(별관 3층)
  • 2024년 07월 03일(수) 13:30
사전등록 바로가기
 

logo

  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

논문 상세

이전 다음
논문 투고

Vol.19 No.4

Citation Share

ASYMPTOTIC BEHAVIORS OF ALTERNATIVE JENSEN FUNCTIONAL EQUATIONS-REVISITED

ASYMPTOTIC BEHAVIORS OF ALTERNATIVE JENSEN FUNCTIONAL EQUATIONS-REVISITED

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2012, v.19 no.4, pp.409-421
https://doi.org/10.7468/jksmeb.2012.19.4.409
Chung, Jaeyoung (Department of Mathematics, Kunsan National University)
Choi, Chang-Kwon (Department of Mathematics, Kunsan National University)
Chung, Jaeyoung, & Choi, Chang-Kwon. (2012). ASYMPTOTIC BEHAVIORS OF ALTERNATIVE JENSEN FUNCTIONAL EQUATIONS-REVISITED. 한국수학교육학회지시리즈B:순수및응용수학, 19(4), 409-421, https://doi.org/10.7468/jksmeb.2012.19.4.409

Abstract

In this paper, using an efficient change of variables we refine the Hyers-Ulam stability of the alternative Jensen functional equations of J. M. Rassias and M. J. Rassias and obtain much better bounds and remove some unnecessary conditions imposed in the previous result. Also, viewing the fundamentals of what our method works, we establish an abstract version of the result and consider the functional equations defined in restricted domains of a group and prove their stabilities.

keywords
Hyers-Ulam stability, Jensen equation, alternative Jensen functional equation, restricted domain

참고문헌

1.

(1950). On the stability of the linear transformation in Banach spaces. J. Math. Soc. Japan, 2, 64-66. 10.2969/jmsj/00210064.

2.

(1951). Class of transformations and bordering transformations. Bull. Amer. Math. Soc., 57, 223-237. 10.1090/S0002-9904-1951-09511-7.

3.

(1950). Multiplicative transformations. Proc. Nat. Academy Sci. of U.S.A., 36, 564-570. 10.1073/pnas.36.10.564.

4.

(0000). Stability of Jensen-type functional equations on restricted domains in a group and their asymptotic behaviors. Journal of Applied Mathematics, 2012.

5.

(1941). On the stability of the linear functional equations. Proc. Nat. Acad. Sci. USA, 27, 222-224. 10.1073/pnas.27.4.222.

6.

(1998). Hyers-Ulam stability of Jensen's equation and its application. Proc. Amer. Math.Soc., 126, 3137-3143. 10.1090/S0002-9939-98-04680-2.

7.

(2005). Asymptotic behavior of alternative Jensen and Jensen type functional equations. Bull. Sci. Math., 129, 545-558. 10.1016/j.bulsci.2005.02.001.

8.

(2003). On the Ulam stability of Jensen and Jensen type mappings on restricted domains. J. Math. Anal. Appl., 281, 516-524. 10.1016/S0022-247X(03)00136-7.

9.

(2002). On the Ulam stability of mixed type mappings on restricted domains. J. Math. Anal. Appl., 276, 747-762. 10.1016/S0022-247X(02)00439-0.

10.

(1978). On the stability of linear mapping in Banach spaces. Proc. Amer. Math. Soc., 72, 297-300. 10.1090/S0002-9939-1978-0507327-1.

11.

(1983). Sull'approssimazione delle applicazioni localmente <TEX>$\delta$</TEX>-additive. Atii Accad. Sci.Torino Cl. Sci. Fis. Mat. Natur., 117, 377-389.

12.

(1983). Proprieta locali e approssimazione di operatori. Rend. Sem. Mat. Fis. Milano, 53, 113-129. 10.1007/BF02924890.

13.

A collection of mathematical problems.

한국수학교육학회지시리즈B:순수및응용수학

논문 투고 OA 정책