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Some inclusion properties of a certain family of integral operators. (English) Zbl 1035.30004
K. I. Noor [J. Nat. Geom. 16, 71–80 (1999; Zbl 0942.30007)] introduced and studied a new class of integral operators associated with analytic functions. This operator is known as Noor integral operator. In this paper, the authors have considered some new classes of analytic functions defined by the generalized Noor integral operator. Using the standard technique, the authors have studied some inclusion properties of these classes. For recent research work on the Noor integral operator, see K. I. Noor and M. A. Noor, J. Math. Anal. Appl. 281, 244–252 (2003; Zbl 1022.30018) and N. E. Cho, J. Math. Anal. Appl. 283, 202–212 (2003; Zbl 1027.30043)]. Also see K. I. Noor, N. Z. J. Math. 24, 53–64 (1995; Zbl 0841.30012), where the linear operator was defined using the hypergeometric function.

MSC:
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
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