Mazur-Ulam Theorem
نویسندگان
چکیده
منابع مشابه
Mazur-Ulam Theorem
The notation and terminology used in this paper have been introduced in the following papers: [19], [18], [4], [5], [20], [11], [10], [14], [17], [1], [6], [16], [24], [25], [21], [13], [12], [22], [2], [9], [8], [3], and [7]. For simplicity, we use the following convention: E, F , G are real normed spaces, f is a function from E into F , g is a function from F into G, a, b are points of E, and...
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The notation and terminology used in this paper have been introduced in the following papers: [19], [18], [4], [5], [20], [11], [10], [14], [17], [1], [6], [16], [24], [25], [21], [13], [12], [22], [2], [9], [8], [3], and [7]. For simplicity, we use the following convention: E, F , G are real normed spaces, f is a function from E into F , g is a function from F into G, a, b are points of E, and...
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In this paper, we give a probabilistic counterpart of Mazur-Ulam theorem in probabilistic normed groups. We show, under some conditions, that every surjective isometry between two probabilistic normed groups is a homomorphism.
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One proves that the Mazur-Ulam theorem can be extended in the framework of metric spaces as long as a well behaved concept of midpoint is available. This leads to the new concept of Mazur-Ulam space. Besides the classical case of real normed spaces, other examples such as Sym++(n,R), the space of all n × n dimensional positive definite matrices, appear as cones attached to suitable Euclidean Jo...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2011
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-011-0020-7