Subordinations and Norm Estimates for Functions Associated with Ma-Minda Subclasses

Aaisha Farzana Habibullah, Muthusamy Palani Jeyaraman and Teodor Bulboacă ()
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Aaisha Farzana Habibullah: Department of Mathematics with Computer Applications, A. M. Jain College, Meenambakkam, Chennai 600061, Tamil Nadu, India
Muthusamy Palani Jeyaraman: Department of Mathematics, L. N. Government College, Ponneri, Chennai 601204, Tamil Nadu, India
Teodor Bulboacă: Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania

Mathematics, 2022, vol. 10, issue 16, 1-16

Abstract: For a function p analytic in the open unit disc and satisfying p ( 0 ) = 1 , we prove certain subordination implications of the first order differential subordination 1 + z p ′ ( z ) ≺ 1 + M z , which provides sufficient conditions for a function to belong to various subclasses of Ma-Minda starlike functions. The pre-Schwarzian norm estimate and inclusion criteria for certain subclasses of analytic function are also obtained. Additionally, using Gronwall’s inequality we give a sufficient condition for a normalized function to belong to a class of functions with bounded arguments that extends the class of strongly α -Bazilevič functions of order γ studied by Gao in 1996.

Keywords: starlike; convex and close-to-convex functions; differential subordination; norm estimate; Schwarzian derivative; pre-Schwarzian derivative; Gronwall’s inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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