On the Sequential Joint (f,δ,q)-Numerical Radius

In this paper, a new sequential joint (f,δ,q)-numerical radius is introduced for sequences of bounded linear operators on Hilbert spaces, motivated by recent generalizations of the numerical radius. Firstly, several fundamental properties of the sequential joint (f,δ,q)-numerical radius function are established. Subsequently, lower and upper bounds for the sequential joint (f,δ,q)-numerical radius function are derived, yielding generalizations of several known inequalities. Finally, the sequential joint (f,δ,q)-numerical radius function is investigated for operator sequences whose coordinate operators are sectorial, leading to further estimates and properties. The obtained results extend and unify a variety of existing results on numerical radius inequalities and provide new contributions to the theory of operator sequences on Hilbert spaces.