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Inclusion properties of a class of functions involving the Dziok-Srivastava operator

H. M. Srivastava|Satwanti Devi|A. Swaminathan
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2016.06|한국수학논문집 (Korean Journal of Mathematics)|제24권 제2호|pp. 139-168|DOI http://dx.doi.org/10.11568/kjm.2016.24.2.139

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참고문헌

키워드

Analytic functionsHohlov operatorCoefficient estimatesGeneralized hypergeometric functionsIntegral transformsDziok- Srivastava linear operatorSrivastava-Wright operatorKomatu operatorPartial sums.
주제분류수학

초록

In this work, we first introduce a class of analytic functions involving the Dziok-Srivastava linear operator that generalizes the class of uniformly starlike functions with respect to symmetric points. We then establish the closure of certain well-known integral transforms under this analytic function class. This behaviour leads to various radius results for these integral transforms. Some of the interesting consequences of these results are outlined. Further, the lower bounds for the ratio between the functions $f(z)$ in the class under discussion, their partial sums $f_m(z)$ and the corresponding derivative functions $f'(z)$ and $f'_m(z)$ are determined by using the coefficient estimates.

Abstract

In this work, we first introduce a class of analytic functions involving the Dziok-Srivastava linear operator that generalizes the class of uniformly starlike functions with respect to symmetric points. We then establish the closure of certain well-known integral transforms under this analytic function class. This behaviour leads to various radius results for these integral transforms. Some of the interesting consequences of these results are outlined. Further, the lower bounds for the ratio between the functions $f(z)$ in the class under discussion, their partial sums $f_m(z)$ and the corresponding derivative functions $f'(z)$ and $f'_m(z)$ are determined by using the coefficient estimates.

참고문헌 (30)

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