3-Variable Additive {\rho} -Functional Inequalities and Equations |
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Authors: | Myeongsu Kim Myeonhu Kim Yeonjun Kim Sanha Lee Choonkil Park |
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Institution: | 1. Mathematics Branch, Seoul Science High School, Seoul, 110-530, Korea 2. Research Institute for Natural Sciences, Hanyang University, Seoul, 133-791, Korea
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Abstract: | In this paper, we introduce and investigate additive \({\rho}\) -functional inequalities associated with the following additive functional equations $$\begin{array}{lll} \,\,\,\,\,\,\, f(x+y+z) - f(x)-f(y)-f(z) \,\,\,\, = 0 \\ 2f \left(\frac{x+y}{2}+z \right) - f(x)-f(y)-2f(z) = 0 \\ \,\,2f \left(\frac{x+y+z}{2} \right) - f(x)-f(y)-f(z) = 0\end{array}$$ Furthermore, we prove the Hyers–Ulam stability of the additive \({\rho}\) -functional inequalities in complex Banach spaces and prove the Hyers–Ulam stability of additive \({\rho}\) -functional equations associated with the additive \({\rho}\) -functional inequalities in complex Banach spaces. |
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