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.

We determine some stability results concerning the pexiderized quadratic functional equation in non-Archimedean fuzzy normed spaces. Our result can be regarded as a generalization of the stability phenomenon in the framework of L-fuzzy normed spaces. AMS Mathematics Subject Classification (2010): 00A11; Primary 46S40; Secondary 39B52, 39B82, 26E50, 46S50.

If there is an order-preserving group isomorphism from a directed abelian group G with a finitely generated positive cone G+ onto a simplicial group, then G is called a semisimplicial group. By factoring out the torsion subgroup of a unital group having a finite unit interval, one obtains a semisimplicial unital group. We exhibit a representation for the base-normed space associated with a semi...

the goal of  this paper is to investigate the solutionand stability in random normed spaces, in non--archimedean spacesand also in $p$--banach spaces and finally the stability using thealternative fixed point of generalized additive functions inseveral variables.

The goal of  this paper is to investigate the solutionand stability in random normed spaces, in non--Archimedean spacesand also in $p$--Banach spaces and finally the stability using thealternative fixed point of generalized additive functions inseveral variables.

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...

Abstract We show that the group of isometries an ultrametric normed space can be seen as a kind fractal. Then, we apply this description to study counterparts some classical problems in Archimedean analysis, such so called Problème des rotations de Mazur or Tingley’s problem. In particular, it turns out that, contrast with case real spaces, between spaces very far from being linear.

In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functional equation f(x+ y) + f(x− y) = 2f(x) + 2f(y) in non-Archimedean L-fuzzy normed spaces.

We investigate a notion of non-Archimedean fuzzy anti-n-normed spaces and prove the Mazur-Ulam theorem in the spaces. AMS subject classification: primary 46S10; secondary 47S10; 26E30; 12J25.