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ISSN : 1226-0657

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Vol.23 No.2
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Quadratic -functional inequalities

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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
LEE, JUNG RYE
SEO, JEONG PIL
YUN,, S. , LEE,, J. R. , & SEO,, J. P. (2016). Quadratic -functional inequalities. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 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

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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