Related papers: Coefficient bounds for starlike functions associat…
We introduce an algorithm to compute the functions belonging to a suitable set ${\mathscr F}$ defined as follows: $f\in {\mathscr F}$ means that $f(s,x)$, $s\in A\subset {\mathbb R}$ being fixed and $x>0$, has a power series expansion…
In the present investigation, we study the class of Sigmoid starlike functions, given by $\mathcal{S}^*_{SG}=\{f\in\mathcal{A}: {zf'(z)}/{f(z)}\prec 2/(1+e^{-z})\}$ in context of estimating the sharp radius constants associated with several…
In this manuscript, we deal with three classes of quotient functions having fixed second coefficient described on open unit disk. The radius of strongly starlikeness, lemniscate starlikeness, lune starlikeness, parabolic starlikeness, sine…
Let A,B,D,E belong to [-1, 1] and let p(z) be an analytic function with fixed initial coefficient defined in the open unit disk. Conditions on A,B,D,and E are determined so that 1+{\alpha}zp'(z) being subordinated to (1+Dz)/(1+Ez) implies…
Let $\mathcal{S}$ denote the class of analytic and univalent functions in $\mathbb{D}:=\{z\in\mathbb{C}:\, |z|<1\}$ of the form $f(z)= z+\sum_{n=2}^{\infty}a_n z^n$. In this paper, we determine sharp estimates for the Toeplitz determinants…
In this short note we prove the logarithmic Sobolev inequality with derivatives of fractional order on $\mathbb{R}^n$ with an explicit expression for the constant. Namely, we show that for all $0<s<\frac{n}{2}$ and $a>0$ we have the…
In this paper, we derive the sharp bounds of Toeplitz determinants for a class of holomorphic mappings on the bounded starlike circular domain $\Omega$ in $\mathbb{C}^n$, which extend certain known bounds for various subclasses of…
In the present paper, the new generalized classes of (p,q)-starlike and $(p,q)$-convex functions are introduced by using the (p,q)-derivative operator. Also, the (p,q)-Bernardi integral operator for analytic function is defined in an open…
In the present article, our goal is finding estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for a new class of bi-univalent functions defined by means of the Horadam polynomials. Fekete-Szego inequalities of functions belonging…
In this work we consider a family of function classes constructed by means of the Gauss hypergeometric function $_2F_1(1,1;2;z) =-\frac{\log(1-z)}{z}$. We demonstrate that this family, in fact, constitutes classes of analytic functions…
In a recent work, we introduced \textit{LC-functions} $L(s,f)$, associated to a certain real-analytic function $f$ at $0$, extending the concept of the Hurwitz zeta function and its formula. In this paper, we establish the existence of a…
In the present investigation the authors obtain upper bounds for the second Hankel determinant of the classes bi-starlike and bi-convex functions of order beta.
Estimation of linear and quadratic functionals over different classes of univalent functions is one of the classical problems in geometric function theory. In this paper we solve the problem over some classes of so-called non-linear…
We investigate the non-univalent function's properties reminiscent of the theory of univalent starlike functions. Let the analytic function $\psi(z)=\sum_{i=1}^{\infty}A_i z^i$, $A_1\neq0$ be univalent in the unit disk. Non-univalent…
In this paper, we study lower bounds of a general family of $L$-functions on the $1$-line. More precisely, we show that for any $F(s)$ in this family, there exists arbitrary large $t$ such that $F(1+it)\geq e^{\gamma_F} (\log_2 t + \log_3…
In this paper, we obtain sharp bounds for the third Hankel determinants of the coefficients of the inverse of bounded turning functions. Thus answering a negatively to a conjecture recently posed regarding these functions. Additionally, we…
For given two harmonic functions $\Phi$ and $\Psi$ with real coefficients in the open unit disk $\mathbb{D}$, we study a class of harmonic functions $f(z)=z-\sum_{n=2}^{\infty}A_nz^{n}+\sum_{n=1}^{\infty}B_n\bar{z}^n$ $(A_n, B_n \geq 0)$…
The logarithmic Sobolev inequality for the Hamming cube {0,1}^n states that for any real-valued function f on the cube holds E(f,f) \ge 2 Ent(f^2), where E(f,f) is the appropriate Dirichlet form (also known as "sum of influences"). We show…
This article investigates the Bohr phenomenon and sharp coefficient problems for the class $\mathcal{A}_{\beta}$, a subclass of analytic self-maps of the unit disk with the holomorphic generators of one-parameter continuous semigroups. By…
In this paper we improve the bounds of the third order Hankel determinant for two classes of univalent functions with bounded turning. The bounds are not sharp, but the sharp ones are conjectured.