Additive \(\rho\)-functional inequalities in fuzzy normed spaces. (English) Zbl 1348.39014

Kim, Ji-Hye; Anastassiou, George A.; Park, Choonkil

J. Comput. Anal. Appl. 21, No. 6, 1115-1126 (2016).

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

Keywords:

fuzzy Banach space; fixed point method; Hyers-Ulam stability; additive \(\rho\)-functional inequalities