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http://dx.doi.org/10.7468/jksmeb.2016.23.2.163

ADDITIVE-QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN FUZZY BANACH SPACES  

LEE, SUNG JIN (DEPARTMENT OF MATHEMATICS, DAEJIN UNIVERSITY)
SEO, JEONG PIL (OHSANG HIGH SCHOOL)
Publication Information
The Pure and Applied Mathematics / v.23, no.2, 2016 , pp. 163-179 More about this Journal
Abstract
Let $M_1f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$, $M_2f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$ Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) $N(M_1f(x,y)-{\rho}M_2f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ and (0.2) $N(M_2f(x,y)-{\rho}M_1f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ in fuzzy Banach spaces, where ρ is a fixed real number with ρ ≠ 1.
Keywords
fuzzy Banach space; additive-quadratic ρ -functional inequality; Hyers-Ulam stability;
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