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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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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: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
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, 23(2), 145-153, https://doi.org/10.7468/jksmeb.2016.23.2.145

Abstract

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