The purpose of this paper is to define q-bounded, semi-bounded, totally bounded, and unbounded sets in an intuitionistic fuzzy metric space X and study the relation between F-bounded sets and the above mentioned sets and prove that the statements (a) X is compact (b) X is sequentially compact and (c) X is complete and totally bounded are all equivalent in an intuitionistic fuzzy metric space X.
Let (S, +) be a semigroup (not necessarily Abelian) and let (X,+) be a commutative group. We deal with an axiomatically given family B ⸦ 2x of "bounded sets" and with mappings f, g, h : S → X such that the transformation S x S ∋ (x, y) → f (x + y) - g (x) - h (y) ∈ X remains B-bounded. Stability results existing in the literature in connection with the Pexider functional equation become special cases of our theorems up to the magnitude of approximating constants.
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