theorem :: RFUNCT_4:15

for a, b being Real
for f, g being PartFunc of REAL,REAL
for X being set st f is_strictly_convex_on X & g is_strictly_convex_on X & ( ( a > 0 & b >= 0 ) or ( a >= 0 & b > 0 ) ) holds
(a (#) f) + (b (#) g) is_strictly_convex_on X