Functional inequalities for the numerical radius

In this paper, we show some new forms of upper bounds for the numerical radii of Hilbert space operators involving a single operator, the product of two and three operators, and off-diagonal operator matrices. The obtained results add a new collection of independent sets that we compare thoroughly with the existing results through numerous examples. Numerical experiments are conducted as there are no explicit relations between the obtained bounds and the existing literature. Thus, these numerical calculations support the non-triviality of the obtained results.