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  • 한국과학기술정보연구원(KISTI) 서울분원 대회의실(별관 3층)
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ISSN : 1226-0657

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Vol.23 No.2
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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
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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

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한국수학교육학회지시리즈B:순수및응용수학

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