Journal of Northeastern University ›› 2013, Vol. 34 ›› Issue (7): 1061-1063.DOI: -

• Mathematics • Previous Articles    

Nonconvex Retracts Constructed by Quasiconvex Functionals

ZHANG Guowei1, ZHAO Tuhua2   

  1. 1. School of Sciences, Northeastern University, Shenyang 110819, China; 2. Institute of Electronic Technology, PLA Information Engineering University, Zhengzhou 450004, China.
  • Received:2014-08-19 Revised:2014-08-19 Online:2013-07-15 Published:2013-12-31
  • Contact: ZHANG Guowei
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Abstract: The nonempty, closed convex subset in Banach space is a retract. Two nonconvex retracts are constructed in Banach spaces by the uniformly continuous nonnegative quasiconvex functional. One of the retracts is a subset of cone, and the other does not need to be restricted in a cone, but needs the infinitedimensional space and the even functional. The earlier results are extended where nonconvex retracts are constructed by the uniformly continuous nonnegative convex functionals and an example is given in the space of continuous functions.

Key words: fixed point, retract, quasiconvex functional, cone, nonconvex

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