This is just a notation question. If I cannot find a preexisting name, I would try onesided convex, or something of the sort.
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closed as offtopic by Pietro Majer, Andrey Rekalo, Stefan Kohl, Alexandre Eremenko, Ricardo Andrade Apr 13 at 0:13This question appears to be offtopic. The users who voted to close gave this specific reason:



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. 

