We introduce the notion of the Gromov-Hausdorff fuzzy distance between two non-Archimedean fuzzy metric spaces (in the sense of Kramosil and Michalek). Basic properties involving convergence and the fuzzy version of the completeness theorem are presented. We show that the topological properties induced by the classic Gromov-Hausdorff distance on metric spaces can be deduced from our approach.

In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functional equation f(x+ y) + f(x− y) = 2f(x) + 2f(y) in non-Archimedean L-fuzzy normed spaces.

The discrete Lotka–Volterra equation over p-adic space was constructed since p-adic space is a prototype of spaces with non-Archimedean valuations and the space given by taking the ultra-discrete limit studied in soliton theory should be regarded as a space with the non-Archimedean valuations given in my previous paper (Matsutani S 2001 Int. J. Math. Math. Sci.). In this paper, using the natura...

We prove that if X,X are closed subschemes of a torus T over a non-Archimedean field K, of complementary codimension and with finite intersection, then the stable tropical intersection along a (possibly positive-dimensional, possibly unbounded) connected componentC of Trop(X)∩Trop(X) lifts to algebraic intersection points, with multiplicities. This theorem requires potentially passing to a suit...