The notion of approximate left φ-biflatness for Banach algebras is introduced, where φ : A −→ C is a non-zero multiplicative linear functional. Under this new concept, the approximate left φ-biflatness for some algebras like group algebras and measure algebras are studied. Moreover, some hereditary properties of this notion are given. Furthermore, some examples to show the differences of our notion and the classical ones are presented.
