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This is just a notation question. If I cannot find a preexisting name, I would try one-sided convex, or something of the sort.

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closed as off-topic by Pietro Majer, Andrey Rekalo, Stefan Kohl, Alexandre Eremenko, Ricardo Andrade Apr 13 at 0:13

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4  
I personally would write "convex in x". –  arsmath Apr 12 at 18:28
4  
and "and continuous in $y$". –  UwF Apr 12 at 18:42

1 Answer 1

up vote 2 down vote accepted

I have not heard the name of such the function (I deal with convex functions)

A function which is continuous wrt. x and wrt. y is called separately convex. Maybe something in this direction.

A function continuous wrt. x and measureble wrt. y is called Caratheodory function. This is another hint.

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