Ho Chong. Function of Region[J]. Applied Mathematics and Mechanics, 1986, 7(2): 173-179.
 Citation: Ho Chong. Function of Region[J]. Applied Mathematics and Mechanics, 1986, 7(2): 173-179.

# Function of Region

• Publish Date: 1986-02-15
• 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.
•  [1] Burkill,J.C.,Function of intervals,Proc.London Math.Soc.,22(1923),275. [2] Enderton,H.B.,Elements of Set Theory,New York(1977). [3] Kirk,R.B.and J.A.Crenshew,A generalized topological measure theory,Trans.Amer.Math Soc.,207,408(1975),189-217. [4] Huard,P.,Optimization algorithm and point-to-set maps,Math.Program,8(1975),308-331. [5] Gurter,M.und H.Weber,Eine verallgemeinerung der Fixpunktsatze ven Ehramann und Schroder for quasimetrische lines-Raume,J.rein.und angew.math.,297(1978),136-162. [6] Spanier,E.,Algebraic Topology,New York(1966). [7] Hartfiel,D.J.,A general theory of measure for nonnegative matrices,Linear Algebra and Appl.,35(1981),21-35.

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