Related papers: A note on a subclass of bazilevi\v{c} functions
A typical quandary in geometric functions theory is to study a functional composed of amalgamations of the coefficients of the pristine function. Conventionally, there is a parameter over which the extremal value of the functional is…
In this article we prove both norm and modular Hardy inequalities for a class functions in one-dimensional fractional Orlicz-Sobolev spaces.
Based on Bohr's equivalence relation which was established for general Dirichlet series, in this paper we introduce a new equivalence relation on the space of almost periodic functions in the sense of Besicovitch,…
In this article we determine the coefficient bounds for functions in certain subclasses of analytic functions defined by subordination which are related to the well-known classes of starlike and convex functions. The main results deal with…
We prove various representations and density results for Hardy spaces of holomorphic functions for two classes of bounded domains in $\mathbb C^n$, whose boundaries satisfy minimal regularity conditions (namely the classes $C^2$ and…
This paper is served as a first contribution regarding the boundedness of Hausdorff operators on function spaces with smoothness. The sharp conditions are established for boundedness of Hausdorff operators on Sobolev spaces $W^{k,1}$. As…
Motivated by G. H. Hardy's 1939 results \cite{Hardy} on functions orthogonal with respect to their real zeros $\lambda_{n}, n=1,2,... $, we will consider, within the same general conditions imposed by Hardy, functions satisfying an…
Let $p \in (1,\infty)$ and $\Omega \subset \mathbb{R}^N$ be a domain. Let $ A: =(a_{ij}) \in L^{\infty}_{\text{loc}}(\Omega; \mathbb{R}^{N\times N})$ be a symmetric and locally uniformly positive definite matrix. Set $|\xi|_A^2:=…
In this paper, we continue our investigation of function spaces on certain classes of complex-valued functions. In particular, we give characterizations on Hardy-type, Bergman-type and Dirichlet-type spaces. Furthermore, we present…
Our primary aim is to explore a sufficient condition for the class of meromorphically convex functions of order $\alpha$, where $0 \leq \alpha < 1$. The investigation will focus on studying a class of continuous functions defined on…
We establish simple pointwise characterizations of functions in the Hardy-Sobolev spaces within the range n/(n+1)<p <=1. In addition, classical Hardy inequalities are extended to the case p <= 1.
In this paper, we determine necessary and sufficient conditions for the generalized Bessel function to be in certain subclasses of starlike and convex functions. Also, we obtain several corollaries as special cases of the main results,…
We build on a characterization of inner functions $f$ due to Le, in terms of the spectral properties of the operator $V=M_f^*M_f$ and study to what extent the cyclicity on weighted Hardy spaces $H^2_\omega$ of the function $z \mapsto a-z$…
Let $\mathcal{B}$ be a homothecy invariant basis consisting of convex sets in $\mathbb{R}^n$, and define the associated geometric maximal operator $M_{\mathcal{B}}$ by $$ M_{\mathcal{B}} f(x) :=\sup_{x \in R \in…
In this paper, we introduce a subclass of p-valent non-bazilavec functions of order. Some subordination relations and the inequality properties of p-valent functions are discussed. The results presented here generalize and improve some…
In this paper, we define the subclasses $R_{\mu,p}^{\delta}(\alpha;A,B)\ $ and $ P_{\mu,p}^{\delta}(\alpha;A,B)\ $ of analytic functions in the open unit disc of complex plain. Then the neighborhood properties, integral means inequalities…
In the present paper, we introduce a new subclass of harmonic functions in the unit disc U defined by using the generalized Mittag-Leffler type functions. Coefficient conditions, extreme points, distortion bounds, convex combination are…
The object of this paper is studying some properties of meromorphic functions which satisfy in the condition \[Re(zf(z)) > \alpha|z^2f'(z)+zf(z)| .\] Parallel results for some related classes are also obtained.
Let $s_{n}(T)$ denote the $n$th approximation, isomorphism, Gelfand, Kolmogorov or Bernstein number of the Hardy-type integral operator $T$ given by $$ Tf(x)=v(x)\int_{a}^{x}u(t)f(t)dt,\,\,\,x\in(a,b)\,\,(-\infty<a<b<+\infty) $$ and mapping…
We say that a function $\alpha(x)$ belongs to the set ${\bf A}^{(\gamma)}$ if it has an asymptotic expansion of the form $\alpha(x)\sim \sum^\infty_{i=0}\alpha_ix^{\gamma-i}$ as $x\to\infty$, which can be differentiated term by term…