  In this paper, we introduce the new notion of strong pseudo-Connes
amenability for dual Banach algebras. We study the relation between this new
notion to the various notions of Connes amenability. Also we show that for
every non-empty set $I$, $M_I(\mathbb{C})$ is strong pseudo-Connes amenable if
and only if $I$ is finite. We provide some examples of certain dual Banach
algebras and we study its strong pseudo-Connes amenability.
  In the last section, we investigate the property ultra central approximate
identity for a Banach algebra $\mathcal{A}$ and its second dual
$\mathcal{A}^{**}$. Also we show that for a left cancellative regular semigroup
$S$, ${\ell^{1}(S)}^{**}$ has an ultra central approximat identity if and only
if $S$ is a group. Finally we study this property for $\varphi$-Lau product
Banach algebras and the module extension Banach algebras.
