Some generalized numerical radius inequalities involving Kwong functions

We prove several numerical radius inequalities involving positive semidefinite matrices via the Hadamard product and Kwong functions. Among other inequalities, it is shown that if X is an arbitrary n x n matrix and A, B are positive semidefinite, then omega(H-f,H-g(A)) <= k omega(AX + XA), which is equivalent to omega(H-f,H- g(A,B) +/- H-f,H- g(B, A)) <= k' {omega((A + B}X + X(A + B)) + omega((A - B)X - X(A - B))}, where f and g are two continuous functions on (0, infinity) such that h(t) = f(t)/g(t) is Kwong, k = max{f(lambda)g(lambda)/lambda : lambda is an element of sigma(A)} and k' = max {f(lambda)g(lambda)/lambda : lambda sigma(A) boolean OR sigma(B)}.