Numerical radius inequalities via convexity

The main goal of this article is to present numerical radius inequalities for matrices based on convexity of certain numerical radius functions. This simple approach extends some unitarily invariant norms inequalities, such as Heinz and Young inequalities, to the context of numerical radius. However, due to weak unitary invariance of the numerical radius, these extended inequalities will be weaker than the corresponding unitarily invariant norms versions.