Additive-cubic functional equations from additive groups into non-Archimedean Banach spaces
نویسندگان
چکیده
منابع مشابه
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 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 $n_x inmathbb{Z}$ such that $x = frac{a}{b}p^{n_x}$, where $a$ and $b$ are integers not divisible by $p$. Then $|x...
متن کاملpositive-additive functional equations in non-archimedean $c^*$-algebras
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 $n_x inmathbb{z}$ such that $x = frac{a}{b}p^{n_x}$, where $a$ and $b$ are integers not divisible by $p$. then $|x...
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In this paper, we solve the additive ρ -functional inequalities ‖ f (x+ y)− f (x)− f (y)‖ ∥∥∥ρ ( 2 f ( x+ y 2 ) − f (x)− f (y) ∥∥∥ (0.1) and ∥∥∥2 f ( x+ y 2 ) − f (x)− f (y) ∥∥∥ ‖ρ ( f (x+ y)− f (x)− f (y))‖ , (0.2) where ρ is a fixed non-Archimedean number with |ρ| < 1 . Furthermore, we prove the Hyers-Ulam stability of the additive ρ -functional inequalities (0.1) and (0.2) in non-Archimedean...
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ژورنال
عنوان ژورنال: Filomat
سال: 2013
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1305731e