In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-Archimedean $mathcal{L}$-fuzzy normed spaces.

In the present paper, a partial order on a non- Archimedean fuzzymetric space under the  Lukasiewicz t-norm is introduced and fixed point theoremsfor single and multivalued mappings are proved.

We study perfect matchings, or close-packed dimer coverings, of finite sections the eleven Archimedean lattices and give a constructive proof showing that any two matchings can be transformed into each other using small sets local ring-exchange moves. This result has direct consequences for formulating quantum models with resonating valence bond ground state, i.e., superposition all coverings c...

Rigorous bounds for the bond percolation critical probability are determined for three Archimedean lattices: .7385 < pc((3, 12 ) bond) < .7449, .6430 < pc((4, 6, 12) bond) < .7376, .6281 < pc((4, 8 ) bond) < .7201. Consequently, the bond percolation critical probability of the (3, 12) lattice is strictly larger than those of the other ten Archimedean lattices. Thus, the (3, 12) bond percolation...

We prove the generalized Ulam stability of ternary homomorphisms from commutative ternary semigroups into n-Banach spaces as well as into complete non-Archimedean normed spaces. Ternary algebraic structures appear in various domains of theoretical and mathematical physics, and p-adic numbers, which are the most important examples of non-Archimedean fields, have gained the interest of physicists...

The representation theorem Cor F-transitive fuzzy relations is used to prove that the set of reflexive, symmetric and F -transitive fuzzy relations on a set X, F being an Archimedean t-norm, is dense in the set of Ztransitive relations on X. It is also shown that any similarity relation can be represented as a limit of a sequence of transitive relations with respect to Archimedean t-norms.

Let G be a connected semisimple group over a non-Archimedean local field. For every faithful, geometrically irreducible linear representation of G we define a compactification of the associated Bruhat-Tits building X(G). This yields a finite family of compactifications of X(G) which contains the polyhedral compactification. Besides, this family can be seen as a non-Archimedean analogue of the f...