### Coefficient inequalities for certain meromorphically $p$-valent functions.

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2000 Mathematics Subject Classification: Primary 30C45, secondary 30C80. We consider some familiar subclasses of functions starlike with respect to symmetric points and obtain sufficient conditions for these classes in terms of their Taylor coefficient. This leads to obtain several new examples of these subclasses.

In a recent paper by H. X. Cao, J. H. Zhang and Z. B. Xu an $\alpha $-Lipschitz operator from a compact metric space into a Banach space $A$ is defined and characterized in a natural way in the sence that $F:K\to A$ is a $\alpha $-Lipschitz operator if and only if for each $\sigma \in {X}^{*}$ the mapping $\sigma \circ F$ is a $\alpha $-Lipschitz function. The Lipschitz operators algebras ${L}^{\alpha}(K,A)$ and ${l}^{\alpha}(K,A)$ are developed here further, and we study their amenability and weak amenability of these algebras. Moreover, we prove an interesting result that ${L}^{\alpha}(K,A)$ and ${l}^{\alpha}(K,A)$ are isometrically...

Let $\mathcal{A}$ be a dual Banach algebra. We investigate the first weak${}^{*}$-continuous cohomology group of $\mathcal{A}$ with coefficients in $\mathcal{A}$. Hence, we obtain conditions on $\mathcal{A}$ for which $${H}_{{w}^{*}}^{1}(\mathcal{A},\mathcal{A})=\left\{0\right\}\phantom{\rule{0.166667em}{0ex}}.$$

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