Related papers: On certain Generalizations of $\mathcal{S}^*(\psi)…
Sufficient conditions on $A$, $B$, $p$, $b$ and $c$ are determined that will ensure the generalized Bessel functions ${u}_{p,b,c}$ satisfies the subordination ${u}_{p,b,c}(z) \prec (1+Az)/ (1+Bz)$. In particular this gives conditions for…
Some geometric properties of a normalized hyper-Bessel functions are investigated. Especially we focus on the radii of starlikeness, convexity, and uniform convexity of hyper-Bessel functions and we show that the obtained radii satisfy some…
In Guo and Peng's article [Spherically convex sets and spherically convex functions, J. Convex Anal. 28 (2021), 103--122], one defines the notions of spherical convex sets and functions on "general curved surfaces" in $\mathbb{R}^{n}$…
In this paper, we investigate three specific subclasses of Ma-Minda type convex functions: namely, convex functions of order $\alpha$, Janowski convex functions, and Robertson functions of normalized analytic functions defined in the open…
We prove that the Bohr' radius for large functions is $e^{-\pi }.$
For $\alpha\geq 0$, $\beta<1$ and $\gamma\geq 0$, the class $\mathcal{W}_{\beta}(\alpha,\gamma)$ satisfies the condition \begin{align*} {\rm Re\,} \left( e^{i\phi}\left((1-\alpha+2\gamma)f/z+(\alpha-2\gamma)f'+ \gamma…
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…
In this paper, some monotonicity and concavity results of several functions involving the psi and polygamma functions are proved, and then some known inequalities are extended and generalized.
We consider three classes of functions defined using the class $\mathcal{P}$ of all analytic functions $p(z)=1+cz+\dotsb$ on the open unit disk having positive real part and study several radius problems for these classes. The first class…
The radii of starlikeness and convexity associated with lemniscate of Bernoulli and the Janowski function, $(1+Az)/(1+Bz)$ for $-1\leq B<A\leq 1$, have been determined for normalizations of $q$-Bessel function, Bessel function of first kind…
Let $\mu$ be a radial compactly supported distribution on a harmonic $NA$ group. We prove that the right convolution operator $c_{\mu}:f \mapsto f* \mu$ maps the space of smooth $\mathfrak{v}$-radial functions onto itself if and only if the…
Let $\mathcal{S}^*(\varphi)$ be the class of all analytic functions $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$, normalized by $f(0)=f'(0)-1=0$ that satisfy the subordination relation $zf'(z)/f(z)\prec\varphi(z)$, where…
In the present paper, the coefficient estimates are found for the class $\mathcal S^{*-1}(\alpha)$ consisting of inverses of functions in the class of univalent starlike functions of order $\alpha$ in $\mathcal D=\{z\in\mathbb C:|z|<1\}$.…
In the past several subclasses of starlike functions are defined involving real part and modulus of certain expressions of functions under study, combined by way of an inequality. In the similar fashion, we introduce a new class…
We obtain sharp estimates for a generalized Zalcman coefficient functional with a complex parameter for the Hurwitz class and the Noshiro-Warschawski class of univalent functions as well as for the closed convex hulls of the convex and…
We show how Lasry-Lions's result on regularization of functions defined on $\mathbb{R}^n$ or on Hilbert spaces by sup-inf convolutions with squares of distances can be extended to (finite or infinite dimensional) Riemannian manifolds $M$ of…
In metric of spaces $L_{s}, \ 1\leq s\leq\infty$, we obtain exact in order estimates of best $m$-term trigonometric approximations of classes of convolutions of periodic functions, that belong to unit all of space $L_{p}, \ 1\leq…
We prove a generalized contraction principle with control function in complete partial metric spaces. The contractive type condition used allows the appearance of self distance terms. The obtained result generalizes some previously obtained…
We produce new upper and lower bounds for the s-Frobenius number by relating it to the so called s-covering radius of a certain convex body with respect to a certain lattice; this generalizes a well-known theorem of R. Kannan for the…
In the present paper, we discuss several basic properties of a class of quasiconformal close-to-convex harmonic mappings with starlike analytic part, such results as coefficient inequalities, an integral representation, a growth theorem, an…