the λ-mean transform of operators

For λ in [0, 1], we introduce the λ-mean transform m_λ(t) of a hilbert space operator t as an extension of some operator transforms based on the duggal transform t^d by m_λ(t) := λt + (1 − λ)t^d and present estimates for the operator norm and .the numerical radius of m_λ(t) in terms of the original operator t