منابع مشابه
Uniform Continuity of Functions on Normed Complex Linear Spaces
For simplicity, we follow the rules: X, X1 denote sets, r, s denote real numbers, z denotes a complex number, R1 denotes a real normed space, and C1, C2, C3 denote complex normed spaces. Let X be a set, let C2, C3 be complex normed spaces, and let f be a partial function from C2 to C3. We say that f is uniformly continuous on X if and only if the conditions (Def. 1) are satisfied. (Def. 1)(i) X...
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 کاملMinimizing Functionals on Normed - linear Spaces
This paper extends results of [1], [2], of Goldstein, and [3] of Vainberg concerning steepest descent and related topics. An example Is given taken from a simple rendezvous problem in control theory. The problem is one of minimizing a norm on an affine subspace. The problem here is solved in the primal. A solution in the dual is given by Neustadt [4]. I. GENERATION OF MINIMIZING SEQUENCES Let E...
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...
متن کاملISOMETRY ON LINEAR n-NORMED SPACES
This paper generalizes the Aleksandrov problem, the Mazur–Ulam theorem and Benz theorem on n-normed spaces. It proves that a one-distance preserving mapping is an nisometry if and only if it has the zero-distance preserving property, and two kinds of n-isometries on n-normed spaces are equivalent.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1993
ISSN: 0022-247X
DOI: 10.1006/jmaa.1993.1112