The Linear Space of Hausdorff Continuous Interval Functions
نویسندگان
چکیده
منابع مشابه
Algebraic operations on the space of Hausdorff continuous interval functions
We show that the operations addition and multiplication on the set C(Ω) of all real continuous functions on Ω ⊆ Rn can be extended to the set H(Ω) of all Hausdorff continuous interval functions on Ω in such a way that the algebraic structure of C(Ω) is preserved, namely, H(Ω) is a commutative ring with identity. The operations on H(Ω) are defined in three different but equivalent ways. This all...
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In the present work we show that the linear operations in the space of Hausdorff continuous functions are generated by an extension property of these functions. We show that the supremum norm can be defined for Hausdorff continuous functions in a similar manner as for real functions, and that the space of all bounded Hausdorff continuous functions on an open set is a normed linear space. Some i...
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The set of interval Hausdorff continuous functions constitutes the largest space preserving basic algebraic and topological structural properties of continuous functions, such as linearity, ring structure, Dedekind order completeness, etc. Spaces of interval functions have important applications not only in the construction of numerical methods and algorithms, but to problems in abstract areas ...
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Hausdorff continuous (H-continuous) functions appear naturally in many areas of mathematics like Approximation Theory [11], Real Analysis [1], [8], Interval Analysis, [2], etc. From numerical point of view it is significant that the solutions of large classes of nonlinear partial differential equations can be assimilated through H-continuous functions [7]. As a particular case the discontinuous...
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ژورنال
عنوان ژورنال: BIOMATH
سال: 2013
ISSN: 1314-7218,1314-684X
DOI: 10.11145/j.biomath.2013.11.261