Journal of Formalized Mathematics
Volume 15, 2003
University of Bialystok
Copyright (c) 2003 Association of Mizar Users

Some Properties for Convex Combinations


Noboru Endou
Gifu National College of Technology
Yasumasa Suzuki
Miyagi University
Yasunari Shidama
Shinshu University, Nagano

Summary.

This is a continuation of [6]. In this article, we proved that convex combination on convex family is convex.

MML Identifier: CONVEX2

The terminology and notation used in this paper have been introduced in the following articles [12] [18] [13] [8] [2] [19] [3] [5] [1] [10] [4] [16] [15] [14] [17] [11] [7] [6] [9]

Contents (PDF format)

  1. Convex Combinations on Convex Family
  2. Miscellaneous

Bibliography

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[13] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[14] Wojciech A. Trybulec. Operations on subspaces in real linear space. Journal of Formalized Mathematics, 1, 1989.
[15] Wojciech A. Trybulec. Subspaces and cosets of subspaces in real linear space. Journal of Formalized Mathematics, 1, 1989.
[16] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.
[17] Wojciech A. Trybulec. Linear combinations in real linear space. Journal of Formalized Mathematics, 2, 1990.
[18] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[19] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received April 3, 2003

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