The purpose of this paper is to extend points function and interval functions theoretics to an arbitrary region. For this, the new theory, the contraction of a region, and the retraction of a region; the extension of a region, and the kernel-preserving extension of a region are established by the author. Starting from these concepts, the new definitions of a region function is given. And a kernel (i.e. fixed point) of a region function is connected with a stable centre of defining region of such a region function. Thereby, the region theoretics and algorithms are established.
In applications, to find a stable centre of a region, the author has utilized the measure theoretics of matrice defined by Hartfiel(7) and other authors. The measure problems of coefficient matrice of system of equations of linear algebra associated with some region are discussed.
KeywordsMathematical Modeling Industrial Mathematic Linear Algebra Region Function Point Function
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- Burkill, J. C., Function of intervals,Proc. London Math. Soc.,22 (1923), 275.Google Scholar
- Enderton, H. B.,Elements of Set Theory, New York (1977).Google Scholar
- Kirk, R. B. and J. A. Crenshew, A generalized topological measure theory,Trans. Amer. Math. Soc.,207, 408 (1975), 189–217.Google Scholar
- Huard, P., Optimization algorithm and point-to-set maps,Math. Program,8 (1975), 308–331.Google Scholar
- Gurter, M. und H. Weber, Eine verallgemeinerung der Fixpunktsatze ven Ehramann und Schroder für quasimetrische lines-Raume,J. rein. und angew. math.,297 (1978), 136–162.Google Scholar
- Spanier, E.,Algebraic Topology, New York (1966).Google Scholar
- Hartfiel, D. J., A general theory of measure for nonnegative matrices,Linear Algebra and Appl.,35 (1981), 21–35.Google Scholar