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Davood Alimohammadi

Davood Alimohammadi

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0002-9398-6213
Education: PhD.
ScopusId: 6505995626
Faculty: Science
Address: Arak University
Phone:

Research

Title
Logarithmic Coefficient Bounds and Coefficient Conjectures for Classes Associated with Convex Functions
Type
JournalPaper
Keywords
Logarithmic Coefficient Bounds, Convex Functions
Year
2021
Journal Journal of Function Spaces
DOI
Researchers Davood Alimohammadi ، Ebrahim Analouee ، Teodor Bulboaka ، Nak Eun Cho

Abstract

It is well-known that the logarithmic coefficients play an important role in the development of the theory of univalent functions. If S denotes the class of functions f ðzÞ = z + Σ∞n=2anzn analytic and univalent in the open unit disk U, then the logarithmic coefficients γnðf Þ of the function f ∈ S are defined by log ðf ðzÞ/zÞ = 2Σ∞n=1γnðf Þzn. In the current paper, the bounds for the logarithmic coefficients γn for some well-known classes like Cð1 + αzÞ for α ∈ ð0, 1 and CVhplð1/2Þ were estimated. Further, conjectures for the logarithmic coefficients γn for functions f belonging to these classes are stated. For example, it is forecasted that if the function f ∈ Cð1 + αzÞ, then the logarithmic coefficients of f satisfy the inequalities jγnj ≤ α/ð2nðn + 1ÞÞ, n ∈ℕ: Equality is attained for the function Lα,n, that is, log ðLα,nðzÞ/zÞ = 2Σ∞n=1γnðLα,nÞzn = ðα/nðn + 1ÞÞzn +⋯,z ∈ U: