Differentiable Functions on Normed Linear Spaces
نویسندگان
چکیده
منابع مشابه
The Differentiable Functions on Normed Linear Spaces
The notation and terminology used in this paper are introduced in the following papers: [20], [23], [4], [24], [6], [5], [19], [3], [10], [1], [18], [7], [21], [22], [11], [8], [9], [25], [13], [15], [16], [17], [12], [14], and [2]. For simplicity, we adopt the following rules: n, k denote natural numbers, x, X, Z denote sets, g, r denote real numbers, S denotes a real normed space, r1 denotes ...
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The terminology and notation used in this paper have been introduced in the following articles: [16], [3], [19], [5], [4], [1], [15], [6], [17], [18], [9], [8], [2], [20], [12], [14], [10], [13], [7], and [11]. For simplicity, we adopt the following rules: S, T denote non trivial real normed spaces, x0 denotes a point of S, f denotes a partial function from S to T , h denotes a convergent to 0 ...
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In this article, we formalize differentiability of functions on normed linear spaces. Partial derivative, mean value theorem for vector-valued functions, continuous differentiability, etc. are formalized. As it is well known, there is no exact analog of the mean value theorem for vector-valued functions. However a certain type of generalization of the mean value theorem for vectorvalued functio...
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The notation and terminology used here have been introduced in the following papers: [12], [2], [3], [7], [9], [11], [1], [4], [10], [13], [6], [17], [18], [15], [8], [16], [19], and [5]. For simplicity, we adopt the following rules: F denotes a non trivial real normed space, G denotes a real normed space, X denotes a set, x, x0, r, p denote real numbers, n, k denote elements of N, Y denotes a ...
متن کاملThe Continuous Functions on Normed Linear Spaces
The articles [16], [19], [20], [2], [21], [4], [9], [3], [1], [11], [15], [5], [17], [18], [10], [7], [8], [6], [13], [22], [12], and [14] provide the notation and terminology for this paper. We use the following convention: n is a natural number, x, X, X1 are sets, and s, r, p are real numbers. Let S, T be 1-sorted structures. A partial function from S to T is a partial function from the carri...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2012
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-012-0005-1