Some subordination results of multivalent functions defined by integral operator. (English) Zbl 1141.30007

The author presents some classes of analytic functions, the Hadamard product and the integral operator was studied by Jung, Kim and Srivastava. Also he presents the definition of differential subordinations and two lemmas of Miller and Mocanu, used in the proofs of the main results. The main results are in the theorems 2.4 and 2.6. The corollaries 2.5 and 2.7 are particular results of these theorems.


30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
Full Text: DOI EuDML


[1] Jung, IB; Kim, YC; Srivastava, HM, The Hardy space of analytic functions associated with certain one-parameter families of integral operators, Journal of Mathematical Analysis and Applications, 176, 138-147, (1993) · Zbl 0774.30008
[2] Shams, S; Kulkarni, SR; Jahangiri, JM, Subordination properties of[inlineequation not available: see fulltext.]-valent functions defined by integral operators, International Journal of Mathematics and Mathematical Sciences, 2006, 3 pages, (2006) · Zbl 1137.30006
[3] Miller SS, Mocanu PT: Differential Subordinations. Theory and Applications, Monographs and Textbooks in Pure and Applied Mathematics. Volume 225. Marcel Dekker, New York, NY, USA; 2000:xii+459.
[4] Liu, J-L; Srivastava, HM, Certain properties of the dziok-Srivastava operator, Applied Mathematics and Computation, 159, 485-493, (2004) · Zbl 1081.30021
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.