On a New Class of Bi-Close-to-Convex Functions with Bounded Boundary Rotation

Daniel Breaz (), Prathviraj Sharma, Srikandan Sivasubramanian and Sheza M. El-Deeb
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Daniel Breaz: Department of Mathematics, “1 Decembrie 1918” University of Alba-Iulia, 510009 Alba Iulia, Romania
Prathviraj Sharma: Department of Mathematics, University College of Engineering Tindivanam, Anna University, Tindivanam 604001, India
Srikandan Sivasubramanian: Department of Mathematics, University College of Engineering Tindivanam, Anna University, Tindivanam 604001, India
Sheza M. El-Deeb: Department of Mathematics, College of Science and Arts, Al-Badaya, Qassim University, Buraidah 52571, Saudi Arabia

Mathematics, 2023, vol. 11, issue 20, 1-16

Abstract: In the current article, we introduce a new class of bi-close-to-convex functions with bounded boundary rotation. For this new class, the authors obtain the first three initial coefficient bounds of the newly defined bi-close-to-convex functions with bounded boundary rotation. By choosing special bi-convex functions, the authors obtain the first three initial coefficient bounds in the last section. The authors also verify the special cases where the familiar Brannan and Clunie’s conjecture is satisfied. Furthermore, the famous Fekete–Szegö inequality is also obtained for this new class of functions. Apart from the new interesting results, some of the results presented here improves the earlier results existing in the literature.

Keywords: analytic; univalent; close-to-convex function of order ?; close-to-convex function; bounded boundary rotations; coefficient estimates; convolution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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