Positive-additive functional equations in non-Archimedean $C^*$-‎algebras‎

Hensel [k. hensel, deutsch. math. verein, 6 (1897), 83-88.] discovered the p-adic number as anumber theoretical analogue of power series in complex analysis. fix a prime number p. for anynonzero rational number x, there exists a unique integer such that x = a, where a andb are integers not divisible by p. then defines a non-archimedean norm on q. thecompletion of q with respect to metric, which is denoted by, is called p-adicnumber field. in fact, p is the set of all formal series x =, here j,p are integersthe addition and multiplication between any two elements of p are defined naturally. the norm x is a non-archimedean norm on p and it makes p a locally compact field. inthis paper, we consider non-archimedean c-algebras and, using the fixed point method, we providean approximation of the positive-additive functional equations in non-archimedean c-algebras.