Furtherance of numerical radius inequalities of Hilbert space operators

If A, B are bounded linear operators on a complex Hilbert space, then we prove that w(A) <= 1/2 (parallel to A parallel to + root r(vertical bar A vertical bar vertical bar A*vertical bar)), w(AB +/- BA) <= 2 root 2 parallel to B parallel to root w(2)(A) - c(2)(R(A) + c(2)(f(A))/2, where w(.), parallel to.parallel to, and r(.) are the numerical radius, the operator norm, the Crawford number, and the spectral radius respectively, and R(A), F(A) are the real part, the imaginary part of A respectively. The inequalities obtained here generalize and improve on the existing well known inequalities.