Some Subclasses of Spirallike Multivalent Functions Associated with a Differential Operator

Ekram Elsayed Ali, Mohamed Kamal Aouf, Rabha Mohamed El-Ashwah and Teodor Bulboacă ()
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Ekram Elsayed Ali: Department of Mathematics, Faculty of Science, University of Hail, Hail 81451, Saudi Arabia
Mohamed Kamal Aouf: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Rabha Mohamed El-Ashwah: Department of Mathematics, Damietta University, New Damietta 34517, Egypt
Teodor Bulboacă: Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania

Mathematics, 2022, vol. 10, issue 17, 1-18

Abstract: In this paper we study convolution properties of spirallike multivalent functions defined by using a differential operator and higher order derivatives. Using convolution product relations we determine necessary and sufficient conditions for multivalent functions to belong to these classes, and our results generalized many previous results obtained by different authors. We obtain convolution and inclusion properties for new subclasses of multivalent functions defined by using the Dziok-Srivatava operator. Moreover, using a result connected with the Briot-Bouquet differential subordination, we obtain an inclusion relation between some of these classes of functions.

Keywords: analytic function; convolution product; generalized hypergeometric function; Dziok-Srivastava linear operator; spirallike function; differential subordination; Briot-Bouquet differential subordination (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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