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Fixed Points Theorems for Mappings with Non-compact and Non-Convex Domains


  • Tian, Guoqiang


This note gives some fixed point theorems for lower and upper semi-continuous mappings and mappings with open lower sections defined on non-compact and non-convex sets. It will be noted that the conditions of our theorems are not only sufficient but also necessary. Also our theorems generalize some well-known fixed point theorems such as the Kakutani fixed point theorem and the Brouwer-Schauder fixed point theorem by relaxing the compactness and convexity conditions.

Suggested Citation

  • Tian, Guoqiang, 1989. "Fixed Points Theorems for Mappings with Non-compact and Non-Convex Domains," MPRA Paper 41299, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:41299

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    References listed on IDEAS

    1. Tian, Guoqiang, 1990. "Equilibrium in abstract economies with a non-compact infinite dimensional strategy space, an infinite number of agents and without ordered preferences," Economics Letters, Elsevier, vol. 33(3), pages 203-206, July.
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    Fixed Points Theorems; Non-compact; Non-Convex; Domains;

    JEL classification:

    • D5 - Microeconomics - - General Equilibrium and Disequilibrium


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