In this work we give a generalization of the results established by W. Ruckle and L. W. Baric for the matrix transformations which preserve schauder basis in the classical case for a p-adic analysis. We give several characterizations of matricial operators which preserve Schauder bases in non archimedean Barrelled spaces. Mathematics Subject Classification: 46A35

Abstract We transfer several elementary geometric properties of rigid-analytic spaces to the world adic spaces, more precisely category which are locally (weakly) finite type over a non-archimedean field. This includes normality, irreducibility (in particular, irreducible components), and Stein factorization theorem. Most notably, we show that morphism in our is automatically open if target nor...

In this work, we define a partial order on probabilistic metric spaces and establish some new Caristi's fixed point theorems Ekeland's variational principle for the class of (right) continuous Archimedean t-norms. As an application, answer to Kirk's problem in is given.

We obtain the general solution of the generalized quartic functional equation f(x + my) + f(x - my) = 2(7m - 9)(m - 1)f(x) + 2m²(m² - 1)f(y)-(m - 1)² f(2x) + m²{f(x + y) + f(x - y)} for a fixed positive integer m. We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the Hyers-Ulam stab...