This paper continues the investigation of Esslamzadeh and the first author which was begun in [ESSLAMZADEH, G. H.-SHOJAEE, B.: Approximate weak amenability of Banach algebras, Bull. Belg. Math. Soc. Simon Stevin 18 (2011), 415-429]. It is shown that homomorphic image of an approximately cyclic amenable Banach algebra is again approximately cyclic amenable. Equivalence of approximate cyclic amenability of a Banach algebra A and approximate cyclic amenability of Mn(A) is proved. It is shown that under certain conditions the approximate cyclic amenability of second dual Aa??a?? implies the approximate cyclic amenability of A.
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机译：本文继续调查Esslamzadeh和第一个作者[Esslamzadeh，G. H.-Shojaee，B.:近似弱扫描Banach代数，公牛。 belg。数学。 SOC。 Simon Stevin 18（2011），415-429]。结果表明，近似环状易用的Banach代数的同态图像再次致循环均匀。证明了Banach代数A和近似循环扫描的Mn（A）的近似循环扫描的等价性。结果表明，在某些条件下，第二双AA的近似循环扫描性a ??意味着A的近似循环扫描性。
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