Sufficient and necessary conditions for the generalized distribution series to be in subclasses of univalent functions

W. Y.  Kota; R. M.  El-Ashwah

doi:10.3842/umzh.v75i10.7267

W. Y. Kota Department of Mathematics, Faculty of Science, Damietta University New Damietta, Egypt
R. M. El-Ashwah Department of Mathematics, Faculty of Science, Damietta University New Damietta, Egypt

DOI: https://doi.org/10.3842/umzh.v75i10.7267

Анотація

УДК 517.5

Достатні та необхідні умови для того, щоб ряди узагальнених розподілів належали до підкласів однолистих функцій

Встановлено зв'язок між підкласами однолистих функцій і рядами узагальнених розподілів. Основною метою цього дослідження є встановлення необхідних і достатніх умов для того, щоб ряди узагальнених розподілів належали до класів ${\mathcal{TF}}(\rho,\vartheta),$ $\mathcal{{TH}}(\rho,\vartheta), \,\mathcal{{TJ}}(\rho,\vartheta)$ і $\mathcal{{TX}}(\rho,\vartheta)$. Крім того, отримано деякі окремі випадки наших основних результатів.

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