Bulletin of the Belgian Mathematical Society - Simon Stevin

A constructive fixed point approach to the existence of a triangle with prescribed angle bisector lengths

George Dinca and Jean Mawhin

Full-text: Open access

Abstract

We show that the use of Brouwer fixed point theorem in Mironescu-Panaitopol's approach to the existence of a triangle with prescribed interior bisector lengths can be replaced by that of Banach fixed point theorem followed by an elementary limiting argument.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 17, Number 2 (2010), 333-341.

Dates
First available in Project Euclid: 26 May 2010

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1274896209

Digital Object Identifier
doi:10.36045/bbms/1274896209

Mathematical Reviews number (MathSciNet)
MR2663476

Zentralblatt MATH identifier
1202.51013

Subjects
Primary: 51M04: Elementary problems in Euclidean geometries 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 01A55: 19th century 01A60: 20th century

Keywords
three bisectors problem Brouwer fixed point theorem Banach fixed point theorem

Citation

Dinca, George; Mawhin, Jean. A constructive fixed point approach to the existence of a triangle with prescribed angle bisector lengths. Bull. Belg. Math. Soc. Simon Stevin 17 (2010), no. 2, 333--341. doi:10.36045/bbms/1274896209. https://projecteuclid.org/euclid.bbms/1274896209


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