superstability of $m$-additive maps on complete non--archimedean spaces
نویسندگان
چکیده
the stability problem of the functional equation was conjectured by ulam and was solved by hyers in the case of additive mapping. baker et al. investigated the superstability of the functional equation from a vector space to real numbers.in this paper, we exhibit the superstability of $m$-additive maps on complete non--archimedean spaces via a fixed point method raised by diaz and margolis.
منابع مشابه
Superstability of $m$-additive maps on complete non--Archimedean spaces
The stability problem of the functional equation was conjectured by Ulam and was solved by Hyers in the case of additive mapping. Baker et al. investigated the superstability of the functional equation from a vector space to real numbers. In this paper, we exhibit the superstability of $m$-additive maps on complete non--Archimedean spaces via a fixed point method raised by Diaz and Margolis.
متن کاملStability of additive mappings in non-Archimedean fuzzy normed spaces
In this paper we introduce a notion of a non-Archimedean fuzzy norm and study the stability of the Cauchy equation in the context of non-Archimedean fuzzy spaces in the spirit of Hyers–Ulam–Rassias–Găvruţa. As a corollary, the stability of the Jensen equation is established. We indeed present an interdisciplinary relation between the theory of fuzzy spaces, the theory of non-Archimedean spaces ...
متن کاملAdditive Ρ –functional Inequalities in Non–archimedean Normed Spaces
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...
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...
متن کاملSystem of AQC functional equations in non-Archimedean normed spaces
In 1897, Hensel introduced a normed space which does not have the Archimedean property. During the last three decades theory of non--Archimedean spaces has gained the interest of physicists for their research in particular in problems coming from quantum physics, p--adic strings and superstrings. In this paper, we prove the generalized Hyers--Ulam--Rassias stability for a ...
متن کاملStability and Superstability of Ring Homomorphisms on Non-Archimedean Banach Algebras
and Applied Analysis 3 Moreover, D. G. Bourgin 16 and Găvruţa 17 have considered the stability problem with unbounded Cauchy differences see also 18–23 . On the other hand, J. M. Rassias 24–29 considered the Cauchy difference controlled by a product of different powers of norm. However, there was a singular case; for this singularity a counterexample was given by Găvruţa 30 . Theorem 1.2 J. M. ...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
sahand communications in mathematical analysisناشر: university of maragheh
ISSN 2322-5807
دوره 2
شماره 1 2015
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023