Functional equation plays a very important and interesting role in the area of mathematics, which involves simple algebraic manipulations through one can arrive an solution. The theory functional equations is also used development other areas such as analysis, algebra, Geometry etc., new methods techniques are applied solving problem Information theory, Finance, Geometry, wireless sensor networ...

We present a p-adic and non-archimedean version of Ahlfors’ Five Islands Theorem for meromorphic functions, extending an earlier theorem of the author for holomorphic functions. In the non-archimedean setting, the theorem requires only four islands, with explicit constants. We present examples to show that the constants are sharp and that other hypotheses of the theorem cannot be removed.

In this paper, we study the geometry of non-Archimedean Gromov-Hausdorff metric. This is the first part of our series work, which we try to establish some facts about the counterpart of Gromov-Hausdorff metric in the non-Archimedean spaces. One of the motivation of this work is to find some implied relations between this geometry and number theory via p-adic analysis, so that we can use the for...

The classical Mazur–Ulam theorem which states that every sur-jective isometry between real normed spaces is affine is not valid for non-Archimedean normed spaces. In this paper, we establish a Mazur–Ulam theorem in the non-Archimedean strictly convex normed spaces.

For a Köthe sequence space, the classes of Λ0-nuclear spaces and spaces with the Λ0-property are introduced and studied and the relation between them is investigated. Also, we show that, for Λ0 6= c0, these classes of spaces are in general different from the corresponding ones for Λ0 = c0, which have been extensively studied in the non-archimedean literature (see, for example, [1]–[6]).

The paper develops techniques in order to construct computer programs, pseudorandom number generators (PRNG), that produce uniformly distributed sequences. The paper exploits an approach that treats standard processor instructions (arithmetic and bitwise logical ones) as continuous functions on the space of 2-adic integers. Within this approach, a PRNG is considered as a dynamical system and is...

For arbitrary real closed fields R, we study the structure of the space M(R(y)) of R-places of the rational function field in one variable over R and determine its dimension to be 1. We determine small subbases for their topology and discuss a suitable metric in the metrizable case. In the case of non-archimedean R, we exhibit the rich variety of homeomorphisms of subspaces that can be found in...

The theme of doing quantum mechanics on all abelian groups goes back to Schwinger and Weyl. If the group is a vector space of finite dimension over a non-archimedean locally compact division ring, it is of interest to examine the structure of dynamical systems defined by Hamiltonians analogous to those encountered over the field of real numbers. In this letter a path integral formula for the im...