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Positivity

, Volume 23, Issue 1, pp 97–100 | Cite as

The Sandwich theorem via Pataraia’s fixed point theorem

  • Massimiliano AmaranteEmail author
Article
  • 54 Downloads

Abstract

The Sandwich theorem (König in Archiv der Mathematik 23:500–1972, 1972) yields the existence of a linear functional sandwiched in between a given superlinear functional and a given sublinear functional. By combining an argument implicit in Fuchssteiner and Maitland Wright (Q J Math 28:155–162, 1977) with a theorem of Pataraia (in: Presented at the 65th peripatetic seminar on sheaves and logic, Aarhus, Denmark, November, 1997), we show that such a linear functional obtains as a common fixed point of a certain family of mappings.

Keywords

Sandwich theorem Pataraia fixed point theorem Inflationary mappings 

Mathematics Subject Classification

46A22 06F20 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Université de Montréal et CIREQMontrealCanada

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