Some generalized numerical radius inequalities for Hilbert space operators

We generalize several inequalities involving powers of the numerical radius for product of two operators acting on a Hilbert space. For any A,B,X∈B(H)A,B,X∈B(H) such that A,BA,B are positive, we establish some numerical radius inequalities for AαXBαAαXBα and AαXB1−αAαXB1−α (0≤α≤10≤α≤1) and Heinz means under mild conditions.