Related papers: On certain Generalizations of $\mathcal{S}^*(\psi)…

Let $\mathcal{H}$ be the space of all functions that are analytic in $\mathbb{D}$. Let $\mathcal{A}$ denote the family of all functions $f\in\mathcal{H}$ and normalized by the conditions $f(0)=0=f'(0)-1$. Obradovi\'{c} and Ponnusamy have…

Let $\mathcal{G}(\alpha)$ denote the family of functions $ f(z)$ in the open unit disk $\mathbb D :=\{z\in\mathbb{C}: |z|<1\}$ that satisfy $ f(0)=0= f'(0)=1$ and \[\Re \left(1+ \dfrac{z f''(z)}{ f'(z)}\right)<1+\dfrac{\alpha}{2} , \quad…

We find two-sides estimates for the best uniform approximations of classes of convolutions of $2\pi$-periodic functions from unit ball of the space $L_p, 1 \le p <\infty,$ with fixed kernels, modules of Fourier coefficients of which satisfy…

The object of the present paper is to study of radius of convexity two certain integral operators as follows \begin{equation*} F(z):=\int_{0}^{z}\prod_{i=1}^{n}\left(f'_i(t)\right)^{\gamma_i}{\rm d}t \end{equation*} and \begin{equation*}…

For $ -1 \leq B \leq 1$ and $A>B$, let $\mathcal{S}^*[A,B]$ denote the class of generalized Janowski starlike functions consisting of all normalized analytic functions $f$ defined by the subordination $z f'(z)/f(z) \prec (1+ A z)/(1+ B z)$…

Geometric function theory increasingly draws on $q$-calculus to model discrete and quantum-inspired phenomena. Motivated by this, the present paper introduces new subclasses of analytic functions: the class $\mathcal{S}^{*}_{\xi_q}$ of…

We introduce a new shape-constrained class of distribution functions on R, the bi-$s^*$-concave class. In parallel to results of D\"umbgen, Kolesnyk, and Wilke (2017) for what they called the class of bi-log-concave distribution functions,…

The Bohr radius for the class of harmonic functions of the form $ f(z)=h+\overline{g} $ in the unit disk $ \mathbb{D}:=\{z\in\mathbb{C} : |z|<1\} $, where $ h(z)=\sum_{n=0}^{\infty}a_nz^n $ and $ g(z)=\sum_{n=1}^{\infty}b_nz^n $ is to find…

Let $A$ be a $C^*$-algebra and $I$ be a closed ideal in $A$. For $x\in A$, its image under the canonical surjection $A\to A/I$ is denoted by $\dot x$, and the spectral radius of $x$ is denoted by $r(x)$. We prove that $$\max\{r(x), \|\dot…

We introduce new shape-constrained classes of distribution functions on R, the bi-$s^*$-concave classes. In parallel to results of D\"umbgen, Kolesnyk, and Wilke (2017) for what they called the class of bi-log-concave distribution…

Let $\mathcal{A}_n$ be the class of analytic functions $f(z)$ of the form $f(z)=z+\sum_{k=n+1}^\infty a_kz^k,n\in\mathbb{N}$ and let \begin{align*} \Omega_n:=\left\{f\in\mathcal{A}_n:\left|zf'(z)-f(z)\right|<\frac{1}{2},\;…

In this paper we determine the radius of convexity for three kind of normalized Bessel functions of the first kind. In the mentioned cases the normalized Bessel functions are starlike-univalent and convex-univalent, respectively, on the…

We consider normalized analytic function $f$ on the open unit disk for which either $\operatorname{Re} f(z)/g(z)>0$, $|f(z) /g(z) - 1|<1$ or $\operatorname{Re} (1-z^2) f(z) /z>0$ for some analytic function $g$ with $\operatorname{Re}…

We find two-sided estimates for Kolmogorov, Bernstein, linear and projection widths of the classes of convolutions of $2\pi$-periodic functions $\varphi$, such that $\|\varphi\|_2\le1$, with fixed generated kernels $\Psi_{\bar{\beta}}$,…

In a recent work of the authors, we showed some general inequalities governing numerical radius inequalities using convex functions. In this article, we present results that complement the aforementioned inequalities. In particular, the new…

We introduce and study a new Ma-Minda subclass of starlike functions $\mathcal{S}^*_{\varrho},$ defined as $$\mathcal{S}^{*}_{\varrho}:=\left\{f\in\mathcal{A}:\frac{zf'(z)}{f(z)} \prec \cosh \sqrt{z}=:\varrho(z), z\in\mathbb{D} \right\},$$…

Let ${\mathcal H}$ denote the class of all normalized complex-valued harmonic functions $f=h+\bar{g}$ in the unit disk ${\mathbb D}$, and let $K=H+\bar{G}$ denote the harmonic Koebe function. Let $a_n,b_n, A_n, B_n$ denote the Maclaurin…

In this paper, we introduce and explore a new class of starlike functions denoted by $\mathcal{S}^*_{\mathfrak{B}}$, defined as follows: $$\mathcal{S}^*_{\mathfrak{B}}=\{f\in \mathcal{A}:zf'(z)/f(z)\prec…

Let $\mathcal{S}^*(\alpha_1,\alpha_2)$, where $ \alpha_1, \alpha_2 \in (0,1]$, represent the class of functions $f$ that are analytic in the open unit disk $\mathbb{D}$, normalized by $f(0) = f'(0) - 1=0$, and satisfying the following…

\noindent In the present investigation, we find the sharp bound of fifth coefficient of analytic normalized function $f$ satisfying $z f'(z)/f(z) \prec \varphi(z)$ when coefficients of $\varphi$ satisfy certain conditions. For an…