Concerning a Novel Integral Operator and a Specific Category of Starlike Functions

Ayotunde Olajide Lasode, Timothy Oloyede Opoola, Isra Al-Shbeil (), Timilehin Gideon Shaba and Huda Alsaud
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Ayotunde Olajide Lasode: Department of Mathematics, Faculty of Physical Sciences, University of Ilorin, P.M.B. 1515, Ilorin 240003, Nigeria
Timothy Oloyede Opoola: Department of Mathematics, Faculty of Physical Sciences, University of Ilorin, P.M.B. 1515, Ilorin 240003, Nigeria
Isra Al-Shbeil: Department of Mathematics, Faculty of Science, The University of Jordon, Amman 11942, Jordan
Timilehin Gideon Shaba: Department of Physical Sciences, Landmark University, Omu-Aran 251103, Nigeria
Huda Alsaud: Department of Mathematics, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia

Mathematics, 2023, vol. 11, issue 21, 1-17

Abstract: In this study, a novel integral operator that extends the functionality of some existing integral operators is presented. Specifically, the integral operator acts as the inverse operator to the widely recognized Opoola differential operator. By making use of the integral operator, a certain subclass of analytic univalent functions defined in the unit disk is proposed and investigated. This new class encompasses some familiar subclasses, like the class of starlike and the class of convex functions, while some new ones are introduced. The investigation thereafter covers coefficient inequality, distortion, growth, covering, integral preserving, closure, subordinating factor sequence, and integral means properties. Furthermore, the radii problems associated with this class are successfully addressed. Additionally, a few remarks are provided, to show that the novel integral operator and the new class generalize some existing ones.

Keywords: analytic function; convex function; coefficient inequality; integral preserving property; radii problems; Opoola differential operator; closure property; distortion property; growth property; subordinating factor sequence property (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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