Simultaneous approximation of additive forms
نویسندگان
چکیده
منابع مشابه
Approximation of an additive mapping in various normed spaces
In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam-Rassias stability of the following Cauchy-Jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem t...
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Let Pd denote the family of all polynomials of degree at most d in one variable x, with real coefficients. A sequence of positive numbers x1 ≤ x2 ≤ . . . is called Pd-controlling if there exist y1, y2, . . . ∈ R such that for every polynomial p ∈ Pd there exists an index i with |p(xi)−yi| ≤ 1. We settle an problem of Makai and Pach (1983) by showing that x1 ≤ x2 ≤ . . . is Pd-controlling if and...
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(1) a1x k 1 + a2x k 2 + · · ·+ asxs = 0 b1x n 1 + b2x n 2 + · · ·+ bsxs = 0, with all coefficients in Q and with s ≥ k + n + 1, then this system should have a nontrivial solution in p-adic integers for each prime p. That is, the system should have a solution with at least one variable not equal to zero. By work of Brauer [3], it is known that there exists a finite bound on s in terms of k and n...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1975
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1975-0366820-7