Some properties of a class of analytic functions involving a new generalized differential operator
Abstract
In the present paper, we introduce a new generalized differential
operator $A_{\mu,\lambda,\sigma}^{m}(\alpha,\beta)$ defined on the open
unit disc $U=\left\{ z\in%
%TCIMACRO{\U{2102} }%
%BeginExpansion
\mathbb{C}:\left\vert z\right\vert <1\right\} $. A novel subclass $\Omega_{m}^{\ast}(\delta,\lambda,\alpha,\beta,b)$ by means of the operator $A_{\mu,\lambda,\sigma}^{m}(\alpha,\beta)$ is also introduced. Coefficient estimates, growth and distortion theorems, closure
theorems, and class preserving integral operators for functions in the class $\Omega_{m}^{\ast}(\delta,\lambda,\alpha,\beta,b)$ are discussed. Furthermore, sufficient conditions for close-to-convexity, starlikeness, and convexity for functions in the class $\Om are obtained
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References
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