Differentiation of Vector-Valued Functions on n-Dimensional Real Normed Linear Spaces
نویسندگان
چکیده
منابع مشابه
Partial Differentiation of Vector-Valued Functions on n-Dimensional Real Normed Linear Spaces
The notation and terminology used in this paper have been introduced in the following papers: [7], [15], [2], [3], [24], [4], [5], [1], [11], [16], [6], [9], [12], [17], [18], [10], [8], [23], [14], [21], [13], and [22]. For simplicity, we use the following convention: n, m denote non empty elements of N, i, j denote elements of N, f denotes a partial function from 〈Em, ‖ · ‖〉 to 〈En, ‖ · ‖〉, g...
متن کاملDifferentiation of Vector-Valued Functions on n-Dimensional Real Normed Linear Spaces
In this paper i, n, m are elements of N. The following propositions are true: (1) Let f be a set. Then f is a partial function from Rm to Rn if and only if f is a partial function from 〈Em, ‖ · ‖〉 to 〈En, ‖ · ‖〉. (2) Let n, m be non empty elements of N, f be a partial function from Rm to Rn, g be a partial function from 〈Em, ‖·‖〉 to 〈En, ‖·‖〉, x be an element of Rm, and y be a point of 〈Em, ‖ ·...
متن کاملPartial Differentiation, Differentiation and Continuity on n-Dimensional Real Normed Linear Spaces
The notation and terminology used in this paper have been introduced in the following papers: [2], [7], [1], [3], [4], [5], [17], [11], [13], [6], [9], [14], [10], [8], [12], and [18]. One can prove the following propositions: (1) Let n, i be elements of N, q be an element of Rn, and p be a point of En T. If i ∈ Seg n and q = p, then |pi| ≤ |q|. (2) For every real number x and for every element...
متن کاملContinuous Functions on Real and Complex Normed Linear Spaces
The notation and terminology used here are introduced in the following papers: [25], [28], [29], [4], [30], [6], [14], [5], [2], [24], [10], [26], [27], [19], [15], [12], [13], [11], [31], [20], [3], [1], [16], [21], [17], [23], [7], [8], [22], [18], and [9]. For simplicity, we use the following convention: n denotes a natural number, r, s denote real numbers, z denotes a complex number, C1, C2...
متن کاملPartial Differentiation on Normed Linear Spaces Rn
Let i, n be elements of N. The functor proj(i, n) yielding a function from Rn into R is defined by: (Def. 1) For every element x of Rn holds (proj(i, n))(x) = x(i). Next we state two propositions: (1) dom proj(1, 1) = R1 and rng proj(1, 1) = R and for every element x of R holds (proj(1, 1))(〈x〉) = x and (proj(1, 1))−1(x) = 〈x〉. (2)(i) (proj(1, 1))−1 is a function from R into R1, (ii) (proj(1, 1...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2010
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-010-0025-7