operator defined on a complex Hilbert space. As a natural application, the existence of the
all polynomial zeros is identified in a specific small disk. Moreover, we provide a refinement
of an earlier numerical radius inequality due to Herzallah et al.[Numerical radius inequalities
for certain 2× 2 operator matrices. Integr Equ Oper Theory. 2011; 71: 129–147] and a
generalization of Shebrawi's inequality [Numerical radius inequalities for certain 2× 2 …