Adam Lecko
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View article: Second Hankel determinant of logarithmic coefficients of inverse strongly starlike functions
Second Hankel determinant of logarithmic coefficients of inverse strongly starlike functions Open
The sharp bound of the second Hankel determinant of logarithmic coefficients of inverse functions of strongly starlike functions is computed.
View article: The second Hankel determinant for logarithmic coefficients of inverse functions of bounded turning of a given order
The second Hankel determinant for logarithmic coefficients of inverse functions of bounded turning of a given order Open
The sharp bound of the second Hankel determinant of logarithmic coefficients of inverse functions of bounded turning of order $$\alpha $$ is computed.
View article: On a logarithmic coefficients inequality for the class of close-to-convex functions
On a logarithmic coefficients inequality for the class of close-to-convex functions Open
In \emph{Logarithmic coefficients problems in families related to starlike and convex functions}, J. Aust. Math. Soc., 109, pp. 230--249, 2020, Ponnusamy et al.\! stated the conjecture for the sharp bounds of the logarithmic coefficients $…
View article: On a Class of Analytic Functions Related to Robertson’s Formula Involving Crescent Shaped Domain and Lemniscate of Bernoulli
On a Class of Analytic Functions Related to Robertson’s Formula Involving Crescent Shaped Domain and Lemniscate of Bernoulli Open
In this paper, we introduce and study the class of analytic functions in the unit disc, which are derived from Robertson’s analytic formula for starlike functions with respect to a boundary point combined with a subordination involving lem…
View article: The second Hankel determinant of the logarithmic coefficients of strongly starlike and strongly convex functions
The second Hankel determinant of the logarithmic coefficients of strongly starlike and strongly convex functions Open
Sharp bounds are given for the second Hankel determinant of the logarithmic coefficients of strongly starlike and strongly convex functions.
View article: A new inner approach for differential subordinations
A new inner approach for differential subordinations Open
In this paper we introduce and examine the differential subordination of the form \[ p(z)+zp'(z)\varphi(p(z),zp'(z))\prec h(z),\quad z\in\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}, \] where $h$ is a convex univalent function with $0\in h(\mathbb…
View article: The third-order Hermitian Toeplitz determinant for some classes of analytic functions
The third-order Hermitian Toeplitz determinant for some classes of analytic functions Open
Sharp lower and upper bounds are found
View article: An evolutionary approach to the coefficient problems in the class of starlike functions
An evolutionary approach to the coefficient problems in the class of starlike functions Open
In this paper, we apply the differential evolution algorithm as a new approach to solve some coefficient problems within Geometric Function Theory. We find sharp bounds for the determinant of the Hankel matrix $H_{4,1}(f)$ and the determin…
View article: Zalcman functional of logarithmic coefficients of inverse functions in certain classes of analytic functions
Zalcman functional of logarithmic coefficients of inverse functions in certain classes of analytic functions Open
We study Hankel matrices whose entries are logarithmic coefficients of inverse functions in selected subclasses of analytic functions. Particularly, we give sharp bounds for the second Hankel determinant which reduces to Zalcman functional…
View article: Sharp Bounds of the Hermitian Toeplitz Determinants for Certain Close-to-Star Functions
Sharp Bounds of the Hermitian Toeplitz Determinants for Certain Close-to-Star Functions Open
The sharp lower and upper bounds of the Hermitian Toeplitz determinants of the second and third order for certain close-to-star functions are computed.
View article: (IN)APPLICABILITY OF STATISTICAL METHODS TO THE STUDIES ON LIVING SYSTEMS: THEORETICAL LENS
(IN)APPLICABILITY OF STATISTICAL METHODS TO THE STUDIES ON LIVING SYSTEMS: THEORETICAL LENS Open
The paper theoretically explores the limitations of the statistical method. Specifically, we point to the inapplicability of statistics in the studies on living systems. Western interdisciplinary sciences, natural sciences and humanities, …
View article: Second Hankel Determinant of Logarithmic Coefficients of Convex and Starlike Functions of Order Alpha
Second Hankel Determinant of Logarithmic Coefficients of Convex and Starlike Functions of Order Alpha Open
In the present paper, we found sharp bounds of the second Hankel determinant of logarithmic coefficients of starlike and convex functions of order $$\alpha $$ .
View article: SECOND HANKEL DETERMINANT OF LOGARITHMIC COEFFICIENTS OF CONVEX AND STARLIKE FUNCTIONS
SECOND HANKEL DETERMINANT OF LOGARITHMIC COEFFICIENTS OF CONVEX AND STARLIKE FUNCTIONS Open
We begin the study of Hankel matrices whose entries are logarithmic coefficients of univalent functions and give sharp bounds for the second Hankel determinant of logarithmic coefficients of convex and starlike functions.
View article: Starlikeness of certain non-univalent functions
Starlikeness of certain non-univalent functions Open
We consider three classes of functions defined using the class $${\mathcal {P}}$$ of all analytic functions $$p(z)=1+cz+\cdots $$ on the open unit disk having positive real part and study several radius problems for these classes. The fi…
View article: On Certain Differential Subordination of Harmonic Mean Related to a Linear Function
On Certain Differential Subordination of Harmonic Mean Related to a Linear Function Open
In this paper we study a certain differential subordination related to the harmonic mean and its symmetry properties, in the case where a dominant is a linear function. In addition to the known general results for the differential subordin…
View article: Sharp Bounds of the Hermitian Toeplitz Determinants for Some Classes of Close-to-Convex Functions
Sharp Bounds of the Hermitian Toeplitz Determinants for Some Classes of Close-to-Convex Functions Open
Sharp upper and lower bounds of the Hermitian Toeplitz determinants of the second and third orders are found for various subclasses of close-to-convex functions.
View article: On a class of analytic functions related to Robertson’s formula and subordination
On a class of analytic functions related to Robertson’s formula and subordination Open
In this paper, we define and study a class of analytic functions in the unit disc by modification of the well-known Robertson’s analytic formula for starlike functions with respect to a boundary point combined with subordination. An integr…
View article: Sharp inequalities for Hermitian Toeplitz determinants for strongly starlike and strongly convex functions
Sharp inequalities for Hermitian Toeplitz determinants for strongly starlike and strongly convex functions Open
Sharp upper and lower bounds are found of the second and third order Hermitian Toeplitz determinants for the classes of strongly starlike and strongly convex functions of order α ( α ∈ [0,1) ).
View article: The fourth-order Hermitian Toeplitz determinant for convex functions
The fourth-order Hermitian Toeplitz determinant for convex functions Open
The sharp bounds for the fourth-order Hermitian Toeplitz determinant over the class of convex functions are computed.
View article: Hermitian Toeplitz determinants of the second and third-order for classes of close-to-star functions
Hermitian Toeplitz determinants of the second and third-order for classes of close-to-star functions Open
For some subclasses of close-to-star functions the sharp upper and lower bounds of the second and third-order Hermitian Toeplitz determinants are computed.
View article: On the fourth and fifth coefficients in the Carathéodory class
On the fourth and fifth coefficients in the Carathéodory class Open
In the paper, we give general parametric formulas for the fourth and fifth coefficients of functions in the Carath?odory class.
View article: Coefficient Problems in the Subclasses of Close-to-Star Functions
Coefficient Problems in the Subclasses of Close-to-Star Functions Open
For two subclasses of close-to-star functions we estimate early logarithmic coefficients, coefficients of inverse functions, Hankel determinant $$H_{2,2}$$ and Zalcman functional $$J_{2,3}$$ . All results are sharp.
View article: SHARP BOUNDS OF SOME COEFFICIENT FUNCTIONALS OVER THE CLASS OF FUNCTIONS CONVEX IN THE DIRECTION OF THE IMAGINARY AXIS
SHARP BOUNDS OF SOME COEFFICIENT FUNCTIONALS OVER THE CLASS OF FUNCTIONS CONVEX IN THE DIRECTION OF THE IMAGINARY AXIS Open
We apply the Schwarz lemma to find general formulas for the third coefficient of Carathéodory functions dependent on a parameter in the closed unit polydisk. Next we find sharp estimates of the Hankel determinant $H_{2,2}$ and Zalcman func…
View article: Subclasses of starlike functions related to Blaschke products
Subclasses of starlike functions related to Blaschke products Open
In this paper we examine subclasses of the class of starlike functions defined by the set of zeros of Schwarz functions. Distortion and the growth theorems are shown. Bounds of the classical coefficient functionals are also computed.
View article: The Bound of the Hankel Determinant of the Third Kind for Starlike Functions
The Bound of the Hankel Determinant of the Third Kind for Starlike Functions Open
In the present paper, the estimate of the third Hankel determinant $$\begin{aligned} \begin{aligned} H_{3,1}(f)&= \begin{vmatrix} a_{1}&a_{2}&a_{3} \\ a_{2}&a_{3}&a_{4} \\ a_{3}&a_{4}&a_{5} \end{vmatrix} \end{aligned} \end{aligned}$$ for t…
View article: Differential subordination of a harmonic mean to a linear function
Differential subordination of a harmonic mean to a linear function Open
In this paper, we examine differential subordination related to the harmonic mean in the case where a dominant is a linear function. A result for the first order Euler differential subordination of the nonlinear type is also discussed.
View article: The Sharp Bound of the Hankel Determinant of the Third Kind for Starlike Functions of Order 1 / 2
The Sharp Bound of the Hankel Determinant of the Third Kind for Starlike Functions of Order 1 / 2 Open
In the present paper, we proved the sharp inequality $$|H_{3,1}(f)|\le 1/9$$ for analytic functions f with $$a_n:=f^{(n)}(0)/n!,\ n\in {\mathbb {N}},\ a_1:=1,$$ such that $$\begin{aligned} {{\mathrm{Re}}}\frac{zf'(z)}{f(z)}> \frac{1}{2},\q…