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Certain New Families for Bi-univalent Functions Defined by a Known Operator
Abbas Kareem Wanas,최준상 영남수학회 2021 East Asian mathematical journal Vol.37 No.3
In this paper, we aim to introduce two new families of analytic and bi-univalent functionsassociated with the Attiya's operator, which is defined by the Hadamard product ofa generalized Mittag-Leffler function and analytic functions on the open unit disk. Then we estimate the second and third coefficients of the Taylor-Maclaurin series expansions of functions belonging to these families. Also, we investigate Fekete-Szeg\"{o} problem for these families. Some relevant connections of certain special cases of the main results with those in several earlier works are also pointed out. Two naturally-arisen problems are given for further investigation.
Srivastava, Hari M.,Wanas, Abbas Kareem Department of Mathematics 2019 Kyungpook mathematical journal Vol.59 No.3
In the present investigation, we define two new subclasses of analytic and m-fold symmetric bi-univalent functions defined by a linear combination in the open unit disk U. Furthermore, for functions in each of the subclasses introduced here, we establish upper bounds for the initial coefficients ${\mid}a_{m+1}{\mid}$ and ${\mid}a_{2m+1}{\mid}$. Also, we indicate certain special cases for our results.
Subclasses of Starlike and Convex Functions Associated with Pascal Distribution Series
Basem Aref Frasin,Sondekola Rudra Swamy,Abbas Kareem Wanas 경북대학교 자연과학대학 수학과 2021 Kyungpook mathematical journal Vol.61 No.1
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.