Fuzzy Functional Analysis—A General View

The concept of fuzzy set introduced by Zadeh in 1965 represented a natural frame for generalizing many of the concepts of Mathematics. The introduction, in 1977, by Katsaras and Liu, of the concept of fuzzy topological vector space resulted in what we call today a new mathematical field “Fuzzy Functional Analysis”. Moreover, Katsaras was the first to introduce the notion of fuzzy norm. From Katsaras onward, many mathematicians (Felbin, Cheng and Mordeson, Bag and Samanta, Saadati and Vaezpour, Goleţ, Nădăban and Dzitac etc.) have proposed several notions of fuzzy norm from different points of view. From the concept of fuzzy normed linear space to the concept of fuzzy normed algebra it is one step that had to be taken. Thus, Sadeqi and Amiripour gave a definition of fuzzy Banach algebra and established some results in this context. Biswas defined the fuzzy inner product of elements in a linear space. Fuzzy operator theory became a hot topic. Recently, fuzzy version of various fixed point theorems was has been discussed in the context of fuzzy normed linear spaces.