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- W2171069389 abstract "1. Introduction and preliminariesIn 1984, Katsaras [17] defined a fuzzy norm on a linear space and at the same year Wuand Fang [32] also introduced a notion of fuzzy normed space and gave the generalizationof the Kolmogoroff normalized theorem for fuzzy topological linear space. In [6], Biswasdefined and studied fuzzy inner product spaces in linear space. Since then some mathe-maticians have defined fuzzy metrics and norms on a linear space from various points ofview [5, 10, 19, 28, 31]. In 1994, Cheng and Mordeson introduced a definition of fuzzynorm on a linear space in such a manner that the corresponding induced fuzzy metric isof Kramosil and Michalek type [18]. In 2003, Bag and Samanta [5] modified the defini-tion of Cheng and Mordeson [7] by removing a regular condition. They also establisheda decomposition theorem of a fuzzy norm into a family of crisp norms and investigatedsome properties of fuzzy norms (see [4]). Following [3], we give the employing notion of afuzzy norm.Let X be a real linear space. A function N : X × R −→ [0,1](the so-called fuzzy subset)is said to be a fuzzy norm on X if for all x,y ∈ X and all a,b ∈ R:(N" @default.
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- W2171069389 date "2009-03-05" @default.
- W2171069389 modified "2023-09-27" @default.
- W2171069389 title "FUZZY STABILITY OF ADDITIVE-QUADRATIC FUNCTIONAL EQUATIONS" @default.
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