Summary: The paper primarily revolves around the convex and V-shaped finite sequences and the inequalities that govern them. We give an elementary proof that a convex sequence is also V-shaped. We prove an inequality that involves an arbitrary nondecreasing function that depends on ceiling functions, thereby establishing the convexity of the corresponding sequence. We present various interpretations and applications of our results, mainly in terms of operations research problems.

convex sequence, V-shaped sequence, ceiling function