in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.

For a point O on the segment AB in the plane, the area surrounded by the three semicircles with diameters AO, BO and AB erected on the same side is called an arbelos. It has lots of unexpected but interesting properties (for an extensive reference see [1]). The radical axis of the inner semicircles divides the arbelos into two curvilinear triangles with congruent incircles called the twin circl...

in the present paper, we give a new approach to caristi's fixed pointtheorem on non-archimedean fuzzy metric spaces. for this we define anordinary metric $d$ using the non-archimedean fuzzy metric $m$ on a nonemptyset $x$ and we establish some relationship between $(x,d)$ and $(x,m,ast )$%. hence, we prove our result by considering the original caristi's fixedpoint theorem.

There are compelling historical and mathematical reasons why we ended up, among others in Physics, with using the scalars given by the real numbers in R, or the complex numbers in C. Recently, however, infinitely many easy to construct and use other algebras of scalars have quite naturally emerged in a number of branches of Applied Mathematics. These algebras of scalars can deal with the long d...

Following the study of sharp domination in effect algebras, in particular, in atomic Archimedean MV-effect algebras it is proved that if an atomic MV-effect algebra is uniformly Archimedean then it is sharply dominating.

Abstract Let G denote a possibly discrete topological group admitting an open subgroup I which is pro- p . If H denotes the corresponding Hecke algebra over field k of characteristic , then we study adjunction between -modules and -linear smooth -representations in terms various model structures. Gorenstein ring, single out full subcategory equivalent to category all projective via functor -inv...

Considering two different metrics on the space of two-dimensional copulas C we prove some Baire category results for important subclasses of copulas, including the families of exchangeable, associative, and Archimedean copulas. From the point of view of Baire categories, with respect to the uniform metric d∞, a typical copula is not symmetric and a typical symmetric copula is not associative, w...

Measures with values in non-Archimedean fields, which are quasi-invariant and descending at infinity on topological vector spaces over non-Archimedean fields, are studied in this paper. Moreover, their characteristic functionals are considered. In particular, measures having convolution properties like classical Gaussian measures are investigated in the paper. Applications of such measures to p...

In Arakelov theory a completion of an arithmetic surface is achieved by enlarging the group of divisors by formal linear combinations of the “closed fibers at infinity”. Manin described the dual graph of any such closed fiber in terms of an infinite tangle of bounded geodesics in a hyperbolic handlebody endowed with a Schottky uniformization. In this paper we consider arithmetic surfaces over t...

In this paper we introduce a notion of a non-Archimedean fuzzy norm and study the stability of the Cauchy equation in the context of non-Archimedean fuzzy spaces in the spirit of Hyers–Ulam–Rassias–Găvruţa. As a corollary, the stability of the Jensen equation is established. We indeed present an interdisciplinary relation between the theory of fuzzy spaces, the theory of non-Archimedean spaces ...