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فهرست مقالات

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

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(7 صفحه - از 179 تا 185)

Hensel [K. Hensel, Deutsch. Math. Verein, 6 (1897), 83-88.] discovered the p-adic number as a number theoretical analogue of power series in complex analysis. Fix a prime number p. for any nonzero rational number x, there exists a unique integer nx 2 Z such that x = a b pnx , where a andb are integers not divisible by p. Then jxjp:= p􀀀nx de nes a non-Archimedean norm on Q. Thecompletion of Q with respect to metric d(x; y) = jx 􀀀 yjp, which is denoted by Qp, is called p-adicnumber eld. In fact, Qp is the set of all formal series x =Σ1 knxakpk, where jakj p􀀀1 are integers.The addition and multiplication between any two elements of Qp are de ned naturally. The norm Σ1knxakpk p= p􀀀nx is a non-Archimedean norm on Qp and it makes Qp a locally compact eld. Inthis paper, we consider non-Archimedean C-algebras and, using the xed point method, we providean approximation of the positive-additive functional equations in non-Archimedean C-algebras.


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