A Class of Bi-Univalent Functions in a Leaf-Like Domain Defined through Subordination via q ̧ -Calculus

Abdullah Alsoboh and Georgia Irina Oros ()
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Abdullah Alsoboh: Department of Mathematics, Faculty of Science, Philadelphia University, Amman 19392, Jordan
Georgia Irina Oros: Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania

Mathematics, 2024, vol. 12, issue 10, 1-15

Abstract: Bi-univalent functions associated with the leaf-like domain within open unit disks are investigated, and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with q -calculus. The class is proved to not be empty. By proving its existence, generalizations can be given to other sets of functions. In addition, coefficient bounds are examined with a particular focus on | α 2 | and | α 3 | coefficients, and Fekete–Szegö inequalities are estimated for the functions in this new class. To support the conclusions, previous works are cited for confirmation.

Keywords: analytic functions; Taylor–Maclaurin coefficients; univalent functions; bi-univalent functions; starlike class; q?-calculus; leaf-like domain; Fekete–Szegö problem; subordination (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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