1.1. Motivation. This paper is largely concerned with constructing quotients by étale equivalence relations. We are inspired by questions in classical rigid geometry, but to give satisfactory answers in that category we have to first solve quotient problems within the framework of Berkovich’s k-analytic spaces. One source of motivation is the relationship between algebraic spaces and analytic s...

In this paper we investigate the generalized Hyers-Ulamstability of the following Cauchy-Jensen type functional equation$$QBig(frac{x+y}{2}+zBig)+QBig(frac{x+z}{2}+yBig)+QBig(frac{z+y}{2}+xBig)=2[Q(x)+Q(y)+Q(z)]$$ in non-Archimedean spaces

In the present paper we prove a unique common fixed point theorem for four weakly compatible self maps in non Archimedean Menger Probabilistic Metric spaces without using the notion of continuity. Our result generalizes and extends the results of Amit Singh, R.C. Dimri and Sandeep Bhatt [A common fixed point theorem for weakly compatible mappings in non-Archimedean Menger PM-space, MATEMATIQKI ...

There is a natural analytification functor from the category of locally separated algebraic spaces locally of finite type over C to the category of complex-analytic spaces [Kn, Ch. I, 5.17ff]. (Recall that a map of algebraic spaces X → S is locally separated if the diagonal ∆X/S : X → X ×S X is an immersion. We require algebraic spaces to have quasi-compact diagonal over SpecZ.) It is natural t...

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.

The aim of this paper is to introduce $n$-variables mappings which are cubic in each variable and to apply a fixed point theorem for the Hyers-Ulam stability of such mapping in non-Archimedean normed spaces. Moreover, a few corollaries corresponding to some known stability and hyperstability outcomes are presented.

The aim of this paper is to prove the uniqueness part of the Calabi–Yau theorem for metrized line bundles over non-archimedean analytic spaces, and apply it to endomorphisms with the same polarization and the same set of preperiodic points over a complex projective variety. The proof uses Arakelov theory (cf. [Ar, GS]) and Berkovich’s non-archimedean analytic spaces (cf. [Be]) even though the r...