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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4$\begingroup$ I personally would write "convex in x". $\endgroup$– arsmathCommented Apr 12, 2014 at 18:28
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4$\begingroup$ and "and continuous in $y$". $\endgroup$– UwFCommented Apr 12, 2014 at 18:42
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1 Answer
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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.
