In metric space we have known about linear mapping and continuousmapping. Both of the mappings have the important properties in normed space. Inthis paper, we study the properties on fuzzy normed space. We start our resultswith first to show that the fuzzy normed space is fuzzy metric space. Then, wedefine the fuzzy continuous mapping and the fuzzy bounded set on fuzzy normedspace. Moreover, we construct the generalisation of properties of relationbetween fuzzy bounded mapping and fuzzy continuous mapping on fuzzy normedspace.
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