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Subclass of p-valent Function with Negative Coefficients Applying Generalized Al-Oboudi Differential Operator

Timilehin G. Shaba, Abd'Gafar T. Tiamiyu, Ismaila O. Ibrahim, Abdullahi A. Ibrahim
Earthline Journal of Mathematical Sciences , Volume 6, pp 87-103; doi:10.34198/ejms.6121.87103

Abstract: In this paper we introduce a new subclass $\mathcal{R}^*(p,g,\psi,\varrho,\beta,\phi,\gamma,\zeta)$ of $p$-valent functions with negative coefficient defined by Hadamard product associated with a generalized differential operator. Radii of close-to-convexity, starlikeness and convexity of the class $\mathcal{R}^*(p,g,\psi,\varrho,\beta,\phi,\gamma,\zeta)$ are obtained. Also, distortion theorem, growth theorem and coefficient inequalities are established.
Keywords: Differential / coefficient / convexity / Hadamard / subclass / theorem / Valent Functions / Starlikeness

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