Abstract
We give Ulam-type stability results concerning the quadratic-additive functional equation in intuitionistic fuzzy normed spaces.
Highlights
In, Ulam [ ] proposed the following stability problem: ‘When is it true that a function which satisfies some functional equation approximately must be close to one satisfying the equation exactly?’
Using the idea of intuitionistic fuzzy set, Saadati and Park [ ] presented the notion of intuitionistic fuzzy normed space which is a generalization of the concept of a fuzzy metric space due to Bag and Samanta [ ]
To prove the uniqueness of T, assume that T is another quadratic-additive mapping from X into Y, which satisfies the required inequality, i.e., ( . )
Summary
In , Ulam [ ] proposed the following stability problem: ‘When is it true that a function which satisfies some functional equation approximately must be close to one satisfying the equation exactly?’. The authors of [ – ] defined and studied some summability problems in the setting of an intuitionistic fuzzy normed space. In this paper we determine the stability results concerning the above functional equation in the setting of intuitionistic fuzzy normed spaces. In this case (μ, ν) is called an intuitionistic fuzzy norm.
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