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.23 No.2

Citation Share

QUADRATIC ρ-FUNCTIONAL INEQUALITIES

Quadratic -functional inequalities

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2016, v.23 no.2, pp.145-153
https://doi.org/10.7468/jksmeb.2016.23.2.145
YUN, SUNGSIK (DEPARTMENT OF FINANCIAL MATHEMATICS, HANSHIN UNIVERSITY)
LEE, JUNG RYE (DEPARTMENT OF MATHEMATICS, DAEJIN UNIVERSITY)
SEO, JEONG PIL (OHSANG HIGH SCHOOL)
YUN, SUNGSIK, LEE, JUNG RYE, & SEO, JEONG PIL. (2016). QUADRATIC ρ-FUNCTIONAL INEQUALITIES. 한국수학교육학회지시리즈B:순수및응용수학, 23(2), 145-153, https://doi.org/10.7468/jksmeb.2016.23.2.145

Abstract

In this paper, we solve the quadratic &#x3C1;-functional inequalities (0.1) <TEX>${\parallel}f(x+y)+f(x-y)-2f(x)-2f(y){\parallel}$</TEX> <TEX>$\leq$</TEX> <TEX>${\parallel}{\rho}(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)){\parallel}$</TEX>, where <TEX>$\rho$</TEX> is a fixed complex number with <TEX>$\left|{\rho}\right|$</TEX> < 1, and (0.2) <TEX>${\parallel}4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y){\parallel}$</TEX> <TEX>$\leq$</TEX> <TEX>${\parallel}{\rho}(f(x+y)+f(x-y)-2f(x)-2f(y)){\parallel}$</TEX>, where &#x3C1; is a fixed complex number with |&#x3C1;| &#x3C; <TEX>$\frac{1}{2}$</TEX>. Furthermore, we prove the Hyers-Ulam stability of the quadratic &#x3C1;-functional inequalities (0.1) and (0.2) in complex Banach spaces.

keywords
Hyers-Ulam stability, quadratic ρ-functional inequality

참고문헌

1.

Park, C.;. (2012). Orthogonal stability of a cubic-quartic functional equation. J. Nonlinear Sci. Appl., 5, 28-36.

2.

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

3.

Ravi, K.;Thandapani, E.;Senthil Kumar, B.V.;. (2014). Solution and stability of a reciprocal type functional equation in several variables. J. Nonlinear Sci. Appl., 7, 18-27.

4.

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

5.

Ulam, S.M.;. A Collection of the Mathematical Problems.

6.

Zaharia, C.;. (2013). On the probabilistic stability of the monomial functional equation. J. Nonlinear Sci. Appl., 6, 51-59.

7.

Hyers, D.H.;. (1941). On the stability of the linear functional equation. Proc. Natl. Acad. Sci. U.S.A, 27, 222-224. 10.1073/pnas.27.4.222.

8.

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

9.

Chahbi, A.;Bounader, N.;. (2013). On the generalized stability of d&#x2019;Alembert functional equation. J. Nonlinear Sci. Appl., 6, 198-204.

10.

Cholewa, P.W.;. (1984). Remarks on the stability of functional equations. Aequationes Math., 27, 76-86. 10.1007/BF02192660.

11.

Eskandani, G.Z.;G&#x1CE;vruta, P.;. (2012). Hyers-Ulam-Rassias stability of pexiderized Cauchy functional equation in 2-Banach spaces. J. Nonlinear Sci. Appl., 5, 459-465.

12.

G&#x1CE;vruta, P.;. (1994). A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings. J. Math. Anal. Appl., 184, 431-436. 10.1006/jmaa.1994.1211.

한국수학교육학회지시리즈B:순수및응용수학

논문 투고 OA 정책