The logarithmic coefficients of functions in the class S

1973 ◽  
Vol 13 (5) ◽  
pp. 793-801 ◽  
Author(s):  
A. Z. Grinshpan
Keyword(s):  
Logarithmic Coefficients

scholarly journals Initial logarithmic coefficients for functions starlike with respect to symmetric points

2021 ◽  
Vol 27 (3) ◽  
Author(s):  
Paweł Zaprawa
Keyword(s):  
Exact Result ◽  
Positive Real Part ◽  
Additional Benefit ◽  
Extremal Functions ◽  
Positive Real ◽  
Logarithmic Coefficients ◽  
Symmetric Points

AbstractIn this paper, we obtain the bounds of the initial logarithmic coefficients for functions in the classes $${\mathcal {S}}_S^*$$ S S ∗ and $${\mathcal {K}}_S$$ K S of functions which are starlike with respect to symmetric points and convex with respect to symmetric points, respectively. In our research, we use a different approach than the usual one in which the coeffcients of f are expressed by the corresponding coeffcients of functions with positive real part. In what follows, we express the coeffcients of f in $${\mathcal {S}}_S^*$$ S S ∗ and $${\mathcal {K}}_S$$ K S by the corresponding coeffcients of Schwarz functions. In the proofs, we apply some inequalities for these functions obtained by Prokhorov and Szynal, by Carlson and by Efraimidis. This approach offers a additional benefit. In many cases, it is easily possible to predict the exact result and to select extremal functions. It is the case for $${\mathcal {S}}_S^*$$ S S ∗ and $${\mathcal {K}}_S$$ K S .

scholarly journals On Coefficient Problems for Functions Connected with the Sine Function

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1179
Author(s):  
Katarzyna Tra̧bka-Wiȩcław
Keyword(s):  
Analytic Functions ◽  
Sine Function ◽  
Hankel Determinant ◽  
Coefficient Problems ◽  
Logarithmic Coefficients ◽  
Symmetric Points

In this paper, some coefficient problems for starlike analytic functions with respect to symmetric points are considered. Bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to find estimates for the following: coefficients, logarithmic coefficients, some cases of the generalized Zalcman coefficient functional, and some cases of the Hankel determinant.

Logarithmic coefficients of univalent functions

1979 ◽  
Vol 36 (1) ◽  
pp. 36-43 ◽  
Author(s):  
P. L. Duren ◽  
Y. J. Leung
Keyword(s):  
Univalent Functions ◽  
Logarithmic Coefficients

scholarly journals Logarithmic Coefficients of the Inverse of Univalent Functions

2018 ◽  
Vol 73 (4) ◽  
Author(s):  
Saminathan Ponnusamy ◽  
Navneet Lal Sharma ◽  
Karl-Joachim Wirths
Keyword(s):  
Univalent Functions ◽  
Logarithmic Coefficients

scholarly journals Certain Coefficient Estimate Problems for Three-Leaf-Type Starlike Functions

2021 ◽  
Vol 5 (4) ◽  
pp. 137
Author(s):  
Lei Shi ◽  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Wali Khan Mashwani ◽  
Praveen Agarwal ◽  
...  
Keyword(s):  
Symmetric Functions ◽  
Starlike Functions ◽  
Upper Bounds ◽  
Coefficient Estimate ◽  
Coefficient Estimates ◽  
Third Order ◽  
Hankel Determinants ◽  
Leaf Type ◽  
Logarithmic Coefficients

In our present investigation, some coefficient functionals for a subclass relating to starlike functions connected with three-leaf mappings were considered. Sharp coefficient estimates for the first four initial coefficients of the functions of this class are addressed. Furthermore, we obtain the Fekete–Szegö inequality, sharp upper bounds for second and third Hankel determinants, bounds for logarithmic coefficients, and third-order Hankel determinants for two-fold and three-fold symmetric functions.

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