Let a,b>=e then we have W(a)+W(b)<=2W(a+b/2)

akuzativo617

akuzativo617

Answered question

2022-11-13

Let a , b e then we have
W ( a ) + W ( b ) 2 W ( a + b 2 )
How to show it for e a b 0 ?

Answer & Explanation

AtticaPlotowvi

AtticaPlotowvi

Beginner2022-11-14Added 18 answers

Changing notations, let a = x + ϵ and b = x ϵ and use series expanion around ϵ = 0. This gives
W ( x + ϵ ) + W ( x ϵ ) = 2 W ( x ) [ W ( x ) x ( W ( x ) + 1 ) ] 2 W ( x ) + 2 W ( x ) + 1 ϵ 2 + O ( ϵ 4 )
which seems to be sufficient.

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