Let X be a non empty normed structure and let s1 be a sequence of X. The functor ( ∑ κ α=0(s1)(α))κ∈N yielding a sequence of X is defined as follows: (Def. 1) ( ∑ κ α=0(s1)(α))κ∈N(0) = s1(0) and for every natural number n holds ( ∑ κ α=0(s1)(α))κ∈N(n + 1) = ( ∑ κ α=0(s1)(α))κ∈N(n) + s1(n + 1). One can prove the following proposition (1) Let X be an add-associative right zeroed right complementa...

in this paper, we study the existence of extremal solutions forimpulsive delay fuzzy integrodifferential equations in$n$-dimensional fuzzy vector space, by using monotone method. weshow that obtained result is an extension of the result ofrodr'{i}guez-l'{o}pez cite{rod2} to impulsive delay fuzzyintegrodifferential equations in $n$-dimensional fuzzy vector space.

Given a normed cone (X , p) and a subcone Y, we construct and study the quotient normed cone (X/Y, p̃) generated by Y . In particular we characterize the bicompleteness of (X/Y, p̃) in terms of the bicompleteness of (X , p), and prove that the dual quotient cone ((X/Y )∗,‖ · ‖p̃,u) can be identified as a distinguished subcone of the dual cone (X∗,‖ · ‖p,u). Furthermore, some parts of the theory ar...

This paper generalizes the Aleksandrov problem, the Mazur–Ulam theorem and Benz theorem on n-normed spaces. It proves that a one-distance preserving mapping is an nisometry if and only if it has the zero-distance preserving property, and two kinds of n-isometries on n-normed spaces are equivalent.

There exists a vast literature about the di erentiabil ity of fuzzy valued mappings see for instance Dubois and Prade Puri and Ralescu Goetschel and Voxman or Kaleva One of the main problems in working with di erentials of fuzzy valued mappings is that the usual class of fuzzy sets of R does not con gure a vectorial space with respect to the sum and the product by a scalar induced by Zadeh s Ex...