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Let (Y, N) be a normed fuzzy Banach space.
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Let X be a normed spaces and (ℝ, N') a fuzzy Banach space.
Definition 2.5 Let ( X, ∥ ⋅ ∥ ) be a normed C ∗ -algebra and N be a fuzzy norm on X. (1) The fuzzy normed ∗-algebra ( X, N ) is called an induced fuzzy normed ∗-algebra.
Definition 2.5 Let ( X, ∥ ⋅ ∥ ) be a normed C ∗ -algebra and N x a fuzzy norm on X. (1) The fuzzy normed ∗-algebra ( X, N x ) is called an induced fuzzy normed ∗-algebra.
Let X be a normed spaces and that (ℝ, N') a fuzzy Banach space.
Corollary 3.3 Let X be a normed space and ( R, N ′ ) be a fuzzy normed space.
Example 1.2 Let ( X, ∥ ⋅ ∥ ) be a normed linear space and let α, β > 0. Then N ( x, t ) = { α t α t + β ∥ x ∥, t > 0, x ∈ X ; 0, t ≤ 0, x ∈ X, is a fuzzy norm on X. Definition 1.3 Let ( X, N ) be a fuzzy normed linear space.
Let (X, N) be a fuzzy normed space and (Y, N') a fuzzy Banach space.
Suppose (A, N) and (B, N) are two fuzzy Banach algebras and (C, N') be a fuzzy normed space.
Let be a fuzzy normed linear space.
Let be a fuzzy normed vector space.
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