In this paper, we give a general solution of a refined quadratic functional equation and then investigate its generalized Hyers–Ulam stability in quasi-normed spaces and in non-Archimedean normed spaces. AMS Subject Classification: 39B82, 39B62

In this article, we introduce a class of the generalized mixed additive, quadratic and quartic functional equations and obtain their common solutions. We also investigate the stability of such modified functional equations in the non-Archimedean normed spaces by a fixed point method.

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...

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.

It is shown that the category of non-Archimedean metric spaces with l-Lipschitz maps can be embedded as a coreflectlve non-bireflective subcategory in the category of fuzzy uniform spaces. Consequential characterizations of topological and unif’orm properties are derived.

We prove that all proper rigid-analytic spaces with “enough” algebraically independent meromorphic functions are algebraic (in the sense of proper algebraic spaces). This is a non-archimedean analogue of a result of Artin over C.