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http://dx.doi.org/10.7468/jksmeb.2017.24.3.179

QUADRATIC (ρ1, ρ2)-FUNCTIONAL INEQUALITY IN FUZZY BANACH SPACES  

Park, Junha (Mathematics Branch, Seoul Science High School)
Jo, Younghun (Mathematics Branch, Seoul Science High School)
Kim, Jaemin (Mathematics Branch, Seoul Science High School)
Kim, Taekseung (Mathematics Branch, Seoul Science High School)
Publication Information
The Pure and Applied Mathematics / v.24, no.3, 2017 , pp. 179-190 More about this Journal
Abstract
In this paper, we introduce and solve the following quadratic (${\rho}_1$, ${\rho}_2$)-functional inequality (0.1) $$N\left(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y),t\right){\leq}min\left(N({\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y)),t),\;N({\rho}_2(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)),t)\right)$$ in fuzzy normed spaces, where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero real numbers with ${{\frac{1}{{4\left|{\rho}_1\right|}}+{{\frac{1}{{4\left|{\rho}_2\right|}}$ < 1, and f(0) = 0. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (${\rho}_1$, ${\rho}_2$)-functional inequality (0.1) in fuzzy Banach spaces.
Keywords
fuzzy Banach space; quadratic (${\rho}_1$, ${\rho}_2$)-functional inequality; fixed point method; Hyers-Ulam stability;
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