In this paper, we utilize group algebras, Fourier algebras, Wiener algebras, and semigroup algebras to present counterexamples that challenge the validity of [4, Proposition 2.10]. Furthermore, we revisit and improve upon their results. In particular, we show that if a Banach algebra A is ϕ-approximately biflat and has a central approximate identity, then A is ϕ-pseudo-amenable.
