Let f,g:[0,1]|->[0,1] becontinuously increasing concave functions such that f(0)=g(0)=0 and f(1)=g(1)=1. I wish to know what is the maximum intersection points between f ad g.

beefypy

beefypy

Answered question

2022-10-31

Let f , g : [ 0 , 1 ] [ 0 , 1 ] becontinuously increasing concave functions such that f ( 0 ) = g ( 0 ) = 0 and f ( 1 ) = g ( 1 ) = 1. What is the maximum intersection points between f ad g.

Answer & Explanation

elulamami

elulamami

Beginner2022-11-01Added 22 answers

It is not true. Take the two piecewise linear continuous functions
f passing by ( 1 / 9 , 4 / 9 ) , ( 5 / 9 , 8 / 9 )
g passing by ( 2 / 9 , 6 / 9 )
They cross at ( 2 / 9 , 5 / 9 ) and ( 4 / 9 , 7 / 9 ).
Using regular polygons centered in ( 1 , 0 ) you may find as many points of intersection as you desire.

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