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ISSN : 1226-0657

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Vol.23 No.3
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Additive ρ-functional inequalities in β-homogeneous F-spaces

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.3, pp.319-328
https://doi.org/10.7468/jksmeb.2016.23.3.319
LEE, HARIN
CHA, JAE YOUNG
CHO, MIN WOO
KWON, MYUNGJUN
LEE,, H. , CHA,, J. Y. , CHO,, M. W. , & KWON,, M. (2016). Additive ρ-functional inequalities in β-homogeneous F-spaces. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 23(3), 319-328, https://doi.org/10.7468/jksmeb.2016.23.3.319
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Abstract

In this paper, we solve the additive &#x3C1;-functional inequalities (0.1) ||f(2x-y)+f(y-x)-f(x)|| <TEX>$\leq$</TEX> ||<TEX>${\rho}(f(x+y)-f(x)-f(y))$</TEX>||, where &#x3C1; is a fixed complex number with |&#x3C1;| &#x3C; 1, and (0.2) ||f(x+y)-f(x)-f(y)|| <TEX>$\leq$</TEX> ||<TEX>${\rho}(f(2x-y)-f(y-x)-f(x))$</TEX>||, where &#x3C1; is a fixed complex number with |&#x3C1;| &#x3C; <TEX>$\frac{1}{2}$</TEX>. Using the direct method, we prove the Hyers-Ulam stability of the additive &#x3C1;-functional inequalities (0.1) and (0.2) in &#x3B2;-homogeneous F-spaces.

keywords
Hyers-Ulam stability, β-homogeneous F-space, additive ρ-functional inequality

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

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