On the Study of Starlike Functions Associated with the Generalized Sine Hyperbolic Function
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Published:2023-12-01
Issue:23
Volume:11
Page:4848
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ISSN:2227-7390
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Container-title:Mathematics
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language:en
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Short-container-title:Mathematics
Author:
Gul Baseer1, Arif Muhammad1ORCID, Alhefthi Reem K.2ORCID, Breaz Daniel3, Cotîrlă Luminiţa-Ioana4ORCID, Rapeanu Eleonora5
Affiliation:
1. Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan 2. Department of Mathematics, College of Sciences, King Saudi University, P.O. Box 2455, Riyadh 11451, Saudi Arabia 3. Department of Mathematics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania 4. Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania 5. Department of Mathematics, “Mircea cel Batran” Naval Academy, 900218 Constanţa, Romania
Abstract
Geometric function theory, a subfield of complex analysis that examines the geometrical characteristics of analytic functions, has seen a sharp increase in research in recent years. In particular, by employing subordination notions, the contributions of different subclasses of analytic functions associated with innovative image domains are of significant interest and are extensively investigated. Since ℜ(1+sinh(z))≯0, it implies that the class Ssinh* introduced in reference third by Kumar et al. is not a subclass of starlike functions. Now, we have introduced a parameter λ with the restriction 0≤λ≤ln(1+2), and by doing that, ℜ(1+sinh(λz))>0. The present research intends to provide a novel subclass of starlike functions in the open unit disk U, denoted as Ssinhλ*, and investigate its geometric nature. For this newly defined subclass, we obtain sharp upper bounds of the coefficients an for n=2,3,4,5. Then, we prove a lemma, in which the largest disk contained in the image domain of q0(z)=1+sinh(λz) and the smallest disk containing q0(U) are investigated. This lemma has a central role in proving our radius problems. We discuss radius problems of various known classes, including S*(β) and K(β) of starlike functions of order β and convex functions of order β. Investigating Ssinhλ* radii for several geometrically known classes and some classes of functions defined as ratios of functions are also part of the present research. The methodology used for finding Ssinhλ* radii of different subclasses is the calculation of that value of the radius r<1 for which the image domain of any function belonging to a specified class is contained in the largest disk of this lemma. A new representation of functions in this class, but for a more restricted range of λ, is also obtained.
Funder
King Saud University in Riyadh, Saudi Arabia
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference30 articles.
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