A property of hyperbolic general family of function spaces with Hadamard gap series

Main Article Content

A. Kamal
T. I. yassen

Abstract

In this article, we obtained results which characterized the hyperbolic general family functions \(F^{*}{(p,q,s)}\) and \(F^{*}_0{(p,q,s)}\) by the coefficients of certain lacunary series expansions in the unit disk. Moreover, we obtain a sufficient and necessary condition for the hyperbolic function \(f^*\) with Hadamard gaps, that is, for \( f(z)= \sum_{k=1}^{\infty} a_{k}z^{n_k}\) satisfying \(\frac{n_{k+1}}{n_k}\geq \lambda > 1\) for all \(k\), to belong to \(F^{*}{(p,q,s)}\) and \(F^{*}_{0}{(p,q,s)}\) on the unite disk \(\mathbb{D}\).

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How to Cite
Kamal, A., & yassen, T. (2018). A property of hyperbolic general family of function spaces with Hadamard gap series. Journal of Advanced Studies in Topology, 9(1), 34–42. https://doi.org/10.20454/jast.2018.1324
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Original Articles