scholarly journals Logarithmic coefficients of starlike functions connected with k-Fibonacci numbers

2021 ◽  
Vol 70 (2) ◽  
pp. 910-923
Author(s):  
Serap BULUT
Keyword(s):  
Fibonacci Numbers ◽  
Starlike Functions ◽  
Logarithmic Coefficients

scholarly journals On a class of starlike functions related to a shell-like curve connected with Fibonacci numbers

2013 ◽  
Vol 57 (5-6) ◽  
pp. 1203-1211 ◽  
Author(s):  
Jacek Dziok ◽  
Ravinder Krishna Raina ◽  
Janusz Sokół
Keyword(s):  
Fibonacci Numbers ◽  
Starlike Functions

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.

scholarly journals On $lambda$-Pseudo Bi-Starlike Functions with Respect to Symmetric Points Associated to Shell-Like Curves

2021 ◽  
Vol 45 (01) ◽  
pp. 103-114
Author(s):  
G. MURUGUSUNDARAMOORTHY ◽  
K. VIJAYA ◽  
H. ÖZLEM GÜNEY
Keyword(s):  
Fibonacci Numbers ◽  
Starlike Functions ◽  
Function Class ◽  
Special Cases ◽  
Symmetric Points

In this paper we define a new subclass λ−pseudo bi-starlike functions with respect to symmetric points of Σ related to shell-like curves connected with Fibonacci numbers and determine the initial Taylor-Maclaurin coefficients |a2| and |a3| for f ∈????????ℒs,Σλ(α,˜p (z)). Further we determine the Fekete-Szegö result for the function class ????????ℒs,Σλ(α,˜p (z)) and for special cases, corollaries are stated which some of them are new and have not been studied so far.

scholarly journals Starlike functions associated with the generalized Koebe function

2021 ◽  
Vol 11 (4) ◽  
Author(s):  
Rahim Kargar ◽  
Lucyna Trojnar-Spelina
Keyword(s):  
Starlike Functions ◽  
Radius Of Starlikeness ◽  
Koebe Function ◽  
Radius Of Convexity ◽  
Logarithmic Coefficients ◽  
Convexity Estimation

AbstractIn this paper we study some properties of functions f which are analytic and normalized (i.e. $$f(0)=0=f'(0)-1$$ f ( 0 ) = 0 = f ′ ( 0 ) - 1 ) such that satisfy the following subordination relation $$\begin{aligned} \left( \frac{zf'(z)}{f(z)}-1\right) \prec \frac{z}{(1-pz)(1-qz)}, \end{aligned}$$ z f ′ ( z ) f ( z ) - 1 ≺ z ( 1 - p z ) ( 1 - q z ) , where $$(p,q) \in [-1,1] \times [-1,1]$$ ( p , q ) ∈ [ - 1 , 1 ] × [ - 1 , 1 ] . These types of functions are starlike related to the generalized Koebe function. Some of the features are: radius of starlikeness of order $$\gamma \in [0,1)$$ γ ∈ [ 0 , 1 ) , image of $$f\left( \{z:|z|<r\}\right) $$ f { z : | z | < r } where $$r\in (0,1)$$ r ∈ ( 0 , 1 ) , radius of convexity, estimation of initial and logarithmic coefficients, and Fekete–Szegö problem.

Some properties associated to a certain class of starlike functions

2019 ◽  
Vol 69 (6) ◽  
pp. 1329-1340 ◽  
Author(s):  
Vali Soltani Masih ◽  
Ali Ebadian ◽  
Sibel Yalçin
Keyword(s):  
Function Theory ◽  
Starlike Functions ◽  
Sharp Inequality ◽  
Open Unit ◽  
Geometric Function Theory ◽  
Open Unit Disk ◽  
Geometric Function ◽  
The Family ◽  
Logarithmic Coefficients ◽  
Dilogarithm Function

Abstract Let 𝓐 denote the family of analytic functions f with f(0) = f′(0) – 1 = 0, in the open unit disk Δ. We consider a class $$\begin{array}{} \displaystyle \mathcal{S}^{\ast}_{cs}(\alpha):=\left\{f\in\mathcal{A} : \left(\frac{zf'(z)}{f(z)}-1\right)\prec \frac{z}{1+\left(\alpha-1\right) z-\alpha z^2}, \,\, z\in \Delta\right\}, \end{array}$$ where 0 ≤ α ≤ 1/2, and ≺ is the subordination relation. The methods and techniques of geometric function theory are used to get characteristics of the functions in this class. Further, the sharp inequality for the logarithmic coefficients γn of f ∈ $\begin{array}{} \mathcal{S}^{\ast}_{cs} \end{array}$(α): $$\begin{array}{} \displaystyle \sum_{n=1}^{\infty}\left|\gamma_n\right|^2 \leq \frac{1}{4\left(1+\alpha\right)^2}\left(\frac{\pi^2}{6}-2 \mathrm{Li}_2\left(-\alpha\right)+ \mathrm{Li}_2\left(\alpha^2\right)\right), \end{array}$$ where Li2 denotes the dilogarithm function are investigated.

scholarly journals An Upper Bound of the Third Hankel Determinant for a Subclass of q-Starlike Functions Associated with k-Fibonacci Numbers

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1043 ◽  
Author(s):  
Muhammad Shafiq ◽  
Hari M. Srivastava ◽  
Nazar Khan ◽  
Qazi Zahoor Ahmad ◽  
Maslina Darus ◽  
...  
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Fibonacci Numbers ◽  
Starlike Functions ◽  
Function Class ◽  
Hankel Determinant ◽  
Derivative Operator ◽  
New Class ◽  
The Third ◽  
Class A

In this paper, we use q-derivative operator to define a new class of q-starlike functions associated with k-Fibonacci numbers. This newly defined class is a subclass of class A of normalized analytic functions, where class A is invariant (or symmetric) under rotations. For this function class we obtain an upper bound of the third Hankel determinant.

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