Some generalized numerical radius inequalities involving Kwong functions

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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× n matrix and A,B are positive semidefinite, then align* ω(Hf,g(A))≤ k ω(AX+XA), align* which is equivalent to align* ω(Hf,g(A,B)± Hf,g(B,A))≤ k'{ω((A+B)X+X(A+B))+ω((A-B)X-X(A-B))}, align* where f and g are two continuous functions on (0,∞) such that h(t)=f(t) g(t) is Kwong, k={f(λ)g(λ) λ: λ∈σ(A)} and k'={f(λ)g(λ) λ: λ∈σ(A)∪σ(B)}.