n this paper we study the Hyers-Ulam-Rassias stability of Cauchyequation in Felbin's type fuzzy normed linear spaces. As a resultwe give an example of a fuzzy normed linear space such that thefuzzy version of the stability problem remains true, while it failsto be correct in classical analysis. This shows how the category offuzzy normed linear spaces differs from the classical normed linearspac...

The concepts of fuzzy θ-open (θ-closed)sets and fuzzy θ-closure operator are introduced and discussed in intuitionistic fuzzy topological spaces. As applications of these concepts, certain functions are characterized in terms of intuitionistic fuzzy θ-closure operator.

We show that the natural mathematical structure to describe a physical entity by means of its states and its properties within the Geneva-Brussels approach is that of a state property system. We prove that the category of state property systems (and morphisms), SP, is equivalent to the category of closure spaces (and continuous maps), Cls. We show the equivalence of the ‘state determination axi...

a new definition of boundedness of linear order-homomorphisms (loh)in $l$-topological vector spaces is proposed. the new definition iscompared with the previous one given by fang [the continuity offuzzy linear order-homomorphism, j. fuzzy math. 5 (4) (1997)829$-$838]. in addition, the relationship between boundedness andcontinuity of lohs is discussed. finally, a new uniform boundednessprincipl...

The categorical theory of closure operators is used to characterize the epimorphisms in certain categories of separated fuzzy topological spaces (in the sense of Lowen). These include the 0-T0-spaces of Wuyts and Lowen; the FTS-spaces of Ghanim, Kerre and Mashhour; and the α-T2-spaces of Rodabaugh.

In this paper, we consider the concepts farthest points and nearest points in normed linear spaces, We obtain a necessary and coecient conditions for proximinal, Chebyshev, remotal and uniquely remotal subsets in normed linear spaces. Also, we consider -remotality, -proximinality, coproximinality and co-remotality.

An idea of fuzzy reexivity of Felbin's type fuzzy normed linear spaces is introduced and its properties are studied. Concept of fuzzy uniform normal structure is given and using the geometric properties of this concept xed point theorems are proved in fuzzy normed linear spaces.

The aim of this paper is to prove the Uniform Boundedness Principle and Banach-Steinhaus Theorem for anti linear operators and hence strong linear operators on Banach hypervector spaces. Also we prove the continuity of the product operation in such spaces.

For Banach spaces X and Y, a bounded linear operator T:X⟶Y⁎ is said to weak-star quasi attains its norm if the σ(Y⁎,Y)-closure of image by T unit ball intersects sphere radius ‖T‖ centered at origin in Y⁎. This notion inspired quasi-norm attainment operators introduced studied [5]. As main result, we prove that set attaining dense space regardless choice spaces, furthermore, approximating can b...

This paper is concerned with an important theorem due to Fyodor L. Zak, which appeared in [Za1]: Let X ⊂ P be a (reduced and irreducible) subvariety. A k – secant space to X is a k – dimensional linear subspace of P which is spanned by k+1 points from X, the k – secant variety of X in P is the (closure of the) union of all the k – secant spaces of X. Zak denotes this space by S(X), we shall als...