@hari_shankar sir please see this..
This is an old Putnam problem
okk sir can you tell the year if u dont mind.i may see solution..thanks sir.
A convex function is a function whose value at the midpoint of the period is less than AM of end pts of the period.
So graphically the sum of areas of starting 2 units and the last 2 units will always be greater than the area between the middle 4 units as the width on x axis is same on both sides but the height in lhs is greater than rhs one
@Samrat_2020 please you share your approch.