In this paper, we investigate the Hyers-Ulam stability for the system of additive, quadratic, cubicand quartic functional equations with constants coecients in the sense of dectic mappings in non-Archimedean normed spaces.

We construct in a rigorous mathematical way interacting quantum field theories on [Formula: see text]-adic spacetime. The main result is the construction of measure function space which allows definition partition function. advantage approach presented here that all perturbation calculations can be carried out standard using functional derivatives, but mathematically way.