The Sandwich theorem via Pataraia’s fixed point theorem
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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.
KeywordsSandwich theorem Pataraia fixed point theorem Inflationary mappings
Mathematics Subject Classification46A22 06F20
- 6.Pataraia, D.: A constructive proof of Tarski’s fixed-point theorem for dcpo’s. Presented at the 65th Peripatetic Seminar on Sheaves and Logic, Aarhus, Denmark, November (1997)Google Scholar