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Additive $$\rho$$-functional inequalities in fuzzy normed spaces. (English) Zbl 1348.39014
Summary: In this paper, we solve the following additive $$p$$-functional inequalities $N (f (x+y)-f (x)-f (y), t) \leq N (\rho(2f ((x +y)/2) - f (x)-f (y)), t)\tag{1}$ and $N (2f ((x+y)/2) - f (x)-f (y),t) \leq N(\rho(f (x+y)-f (x)-f (y)),t)\tag{2}$ in fuzzy normed spaces, where $$\rho$$ is a fixed real number with $$|\rho|< 1$$. Using the fixed point method, we prove the Hyers-Ulam stability of the additive $$\rho$$-functional inequalities (1) and (2) in fuzzy Banach spaces.

##### MSC:
 39B62 Functional inequalities, including subadditivity, convexity, etc. 39B52 Functional equations for functions with more general domains and/or ranges 46S40 Fuzzy functional analysis 39B82 Stability, separation, extension, and related topics for functional equations