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Note on Generalized Convex Spaces

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Book cover Nonlinear Mathematics for Uncertainty and its Applications

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 100))

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Abstract

Some examples are given to show that some known generalized convex spaces are so abstract that some basic properties related to the convexity are lost. In order to improve the convexity structure for applications, the concepts of path-convex space, path-convex set and path-convex function are introduced. And their properties are discussed.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Beijing University of Technology, Beijing, 100124, P.R. China

    Xiaodong Fan

  2. College of Elect & Control Engineering, Beijing University of Technology, Beijing, 100124, P.R. China

    Yue Cheng

Authors
  1. Xiaodong Fan
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  2. Yue Cheng
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Editor information

Editors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, 100124, Chaoyang District, Beijing, P.R. China

    Shoumei Li , Xia Wang  & Li Guan ,  & 

  2. Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4, Kawazu, 820-8502, lizuka, Japan

    Yoshiaki Okazaki

  3. Department of Mathematics, Shinshu University, 4-17-1 Wakasato, 380-8553, Nagano, Japan

    Jun Kawabe

  4. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47, Nagatsuta, Midori-ku, 226-8502, Yokohama, Japan

    Toshiaki Murofushi

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© 2011 Springer-Verlag Berlin Heidelberg

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Fan, X., Cheng, Y. (2011). Note on Generalized Convex Spaces. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_46

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  • DOI: https://doi.org/10.1007/978-3-642-22833-9_46

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

  • eBook Packages: EngineeringEngineering (R0)

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