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Subclasses of Starlike and Convex Functions Associated with Pascal Distribution Series

Abbas Kareem Wanas|Basem Aref Frasin|Sondekola Rudra Swamy
경북대학교 자연과학대학 수학과|2021.03|Kyungpook Mathematical Journal|제61권 제1호|pp. 99-110

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참고문헌

키워드

Analytic functionsHadamard productPascal distribution series
주제분류수학

초록

In the present paper, we determine new characterisations of the subclasses TS∗C(α, β; γ) and TCC(α, β; γ) of analytic functions associated with Pascal distribution series Φm q (z) = z −R∞ n=2 (n+m−2 m−1)qn−1(1 − q)m(z)n. Further, we give necessary and sufficient conditions for an integral operator related to Pascal distribution series Gmq f(z) = R z 0 Φmq (t)t dt to belong to the above classes. Several corollaries and consequences of the main results are also considered.

Abstract

In the present paper, we determine new characterisations of the subclasses TS∗C(α, β; γ) and TCC(α, β; γ) of analytic functions associated with Pascal distribution series Φm q (z) = z −R∞ n=2 (n+m−2 m−1)qn−1(1 − q)m(z)n. Further, we give necessary and sufficient conditions for an integral operator related to Pascal distribution series Gmq f(z) = R z 0 Φmq (t)t dt to belong to the above classes. Several corollaries and consequences of the main results are also considered.

참고문헌 (23)

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