8,877 Results Found

In this paper, we consider the simultaneous approximation of tuples of analytic functions by tuples of shifts of Lerch zeta-functions with arbitrary parameters. We prove that there exists a closed set of tuples of functions analytic in the right-hand...

Let the class of functions of $f\left(z\right)$ of the form $f\left(z\right)=z+{\sum }_{k=2}^{\infty }{a}_k{z}^k$, which are denoted by $\mathcal{A}$ and called analytic functions in the open-unit disk. There are many interesting properties of the functions $f\left(z\right)$ in the class $\mathcal{A}$ concerning the subordina...

Estimates bounds for Carathéodory functions in the complex domain are applied to demonstrate sharp limits for the inverse of analytic functions. Determining these values is considered a more difficult task compared to finding the values of ana...

The normalized analytic function ${\Phi }_N\left(z\right)=1+z-{\displaystyle \frac{z^3}{3}}$, which connects the open unit disk onto a bounded domain within the right half of a nephroid-shaped region, is associated with the bounded turning of functions denoted by $R_n$. It calculates the...

In the present paper, we consider the class $\overline{\mathcal{A}}$ of functions $f\left(z\right)$ of the form $f\left(z\right)=z+{\sum }_{k=1}^{\infty }{a}_{1+\frac{k}{3}}{z}^{1+\frac{k}{3}}$ that are analytic in the open unit disc $\mathbb{U}.$ If $a_{1+\frac{k}{3}}=0$ for $k\ne 3n$$(n=1,2,3,\cdots ),$ then $f\left(z\right)$ is given by $f\left(z\right)=z+{\sum }_{k=2}^{\infty }{a}_k{z}^k.$ F...

For $j=1,\dots ,r$, let ${\mathcal{P}}_j$ be a system of generalized prime numbers, ${\mathcal{N}}_{{\mathcal{P}}_j}$ the corresponding system of generalized integers, and ${\zeta }_{{\mathcal{P}}_j}\left(s\right)$, $s=\sigma +it$, the Beurling zeta-function. In the paper, we consider simultaneous approximation of a collection...

The purpose of this research is to unify and extend the study of the well-known concept of coefficient estimates for some subclasses of analytic functions. We define the new subclass ${\mathcal{A}}_4^{r,s}$ of analytic functions related to the four-leaf domain, to inc...

The Lerch zeta function is defined by a Dirichlet series depending on two fixed parameters. In the paper, we consider the approximation of analytic functions by discrete shifts of the Lerch zeta function, and we prove that, for arbitrary parameters a...

In this paper, a new operator $D^{s}f$, with s a real number, is defined considering functions that belong to the known class of p-valent analytic functions in the open unit disk U. Applying this operator, a new subclass of p-valently analytic functions i...

For the analytic functions $\varphi \left(\zeta \right)=\zeta +{\sum }_{k=n}^{\infty }{\varphi }_k{\zeta }^k$ in the unit disk $\mathbb{O},$ we calculate the values of n and $\alpha ,$ where the condition $\Re \left(1+\zeta {\varphi }^{″}\left(\zeta \right)/{\varphi }^{\prime }\left(\zeta \right)\right)>-\alpha$ or $\Re \left(1+\mathrm{\&z}\right)$...

In the paper, we obtain universality theorems for compositions of some classes of operators in multidimensional space of analytic functions with a collection of periodic zeta-functions. The used shifts of periodic zeta-functions involve the sequence...

In the paper, we study various countably generated algebras of entire analytic functions on complex Banach spaces and their homomorphisms. Countably generated algebras often appear as algebras of symmetric analytic functions on Banach spaces with res...

Let $\mathfrak{B}$ denote the class of bounded turning functions $\mathcal{F}$ analytic in the open unit disk, where the image of ${\mathcal{F}}^{\prime }\left(z\right)$ is contained in the domain $\Omega \left(z\right)=\cosh z+{\displaystyle \frac{2z}{2-z^2}}$. This article determines sharp coefficient bounds, a Fekete–Szegö...

One of the fundamental parts of Geometric Function Theory is the study of analytic functions in different domains with critical geometrical interpretations. This article defines a new generalized domain obtained based on the quotient of two analytic...

Let $\overline{\mathcal{A}}$ be the new general class of functions $f\left(z\right)$ of the form $f\left(z\right)=z+{\displaystyle \sum _{k=1}^{\infty }}{a}_{1+\frac{k}{2}}{z}^{1+\frac{k}{2}}$ that are analytic in the open unit disc $\mathbb{U}.$ In the present paper, for $f\left(z\right)\in \overline{\mathcal{A}},$ we consider classes $\overline{{\mathcal{S}}^{\ast }}\left(\alpha \right),$ $\overline{\mathcal{C}}(\mathrm{\&al}$...

In this paper we investigate analytic functions of unbounded type on a complex infinite dimensional Banach space $X.$ The main question is: under which conditions is there an analytic function of unbounded type on X such that its Taylor polynomials are...

In this contribution, we define a new operator sequence which contains analytic functions. Using approximation techniques found by Korovkin, some results are derived. Moreover, a generalization of this operator sequence called Kantorovich type genera...

This study examines the necessary requirements for some analytic function subclasses, especially those associated with the generalized Mittag-Leffler function, to be classified as univalent function subclasses that are determined by particular geomet...

The goal of this article is to contemplate coefficient estimates for a new class of analytic functions f associated with generalized telephone numbers to originate certain initial Taylor coefficient estimates and Fekete–Szegö inequality fo...

This paper introduces a novel class of analytic functions that integrates q-calculus, Janowski-type functions, and (a, b)-symmetrical functions. By exploring convolution operations and quantum calculus, we establish essential convolution conditions t...

In this paper, we consider a subclass $\mathcal{SQ}$ of normalized analytic functions f satisfying $\Re \sqrt{f^{\prime }\left(z\right)}>1/2$. For the functions in the class $\mathcal{SQ}$, we determine upper bounds for a number of coefficient estimates, among which are initial coefficients,...

The coefficient problem is an essential topic in the theory of univalent functions theory. In the present paper, we consider a new subclass $\mathcal{SQ}$ of analytic functions with $f^{\prime }\left(z\right)$ subordinated to $1/{(1-z)}^2$ in the open unit disk. This class was...

First, by making use of the concept of basic (or q-) calculus, as well as the principle of subordination between analytic functions, generalization ${\mathcal{R}}_q\left(h\right)$ of the class $\mathcal{R}\left(h\right)$ of analytic functions, which are associated with the leaf-like domain in the o...

This paper is devoted to the study of the algebra of bounded-type block-symmetric analytic functions on the Banach space ${\mathcal{l}}_1\left({\mathbb{C}}^s\right).$ In particular, it presents a description of the spectrum of this algebra in terms of exceptional characters ${\varphi }_{\alpha }$...

A class of p-valent analytic functions is introduced using the q-difference operator and the familiar Janowski functions. Several properties of functions in the class, such as the Fekete–Szegö inequality, coefficient estimates, necessary and sufficie...

A sequence of n trials from a finite population with no replacement is described by the hypergeometric distribution as the number of successes. Calculating the likelihood that factory-produced items would be defective is one of the most popular uses...

In this paper, we introduce a new class of analytic functions, denoted by $\mathfrak{S}(\nu ,{\phi }_{\vartheta ,e})$, and provide illustrative examples to elucidate its properties. This class generalizes the starlike and convex functions previously defined by Khatter...

Recently, we established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of analytical function to obtain new criteria equivalent to the Riemann hypothesis. The same theorem was subsequently applied to calcul...

The main purpose of this work is to study the third Hankel determinant for classes of Bernoulli lemniscate-related functions by introducing new subclasses of star-like functions represented by $S_{L\lambda }^{*}$ and $R{L}_{\lambda }$. In many geometric and physica...

In the present paper, we have introduced a new subclass of analytic functions involving integral operator defined by polylogarithm function. Necessary and sufficient conditions are obtained for this class. Further distortion theorem, linear combinati...

This paper focuses on the establishment of a new subfamily of analytic functions including Touchard polynomials. Then, we attempt to obtain geometric properties such as coefficient inequalities, distortion properties, extreme points, radii of starlik...

Fractional calculus has a number of applications in the field of science, specially in mathematics. In this paper, we discuss some applications of fractional differential operators in the field of geometric function theory. Here, we combine the fract...

In the paper we establish some conditions under which a given sequence of polynomials on a Banach space X supports entire functions of unbounded type, and construct some counter examples. We show that if X is an infinite dimensional Banach space, the...

In this article we introduced and studied some inclusion properties for new subclasses of multivalent analytic functions defined by using the q-derivative operator. With the aid of the Jackson q-derivative we defined two new operators that generalize...

The zero-truncated Poisson distribution is an important and appropriate model for many real-world applications. Here, we exploit the zero-truncated Poisson distribution probabilities to construct a new subclass of analytic bi-univalent functions invo...

This paper explores a class of analytic functions defined in the open unit disk by means of a symmetric q-differential operator. In the first part, we derive sufficient conditions for functions to belong to a subclass associated with this operator, u...

The study done for obtaining the original results of this paper involves the fractional integral of the confluent hypergeometric function and presents its new applications for introducing a certain subclass of analytic functions. Conditions for funct...

By using the generalization of the neutrosophic q-Poisson distribution series, we introduce a new subclass of analytic and bi-univalent functions defined in the open unit disk. We then apply the q-Gegenbauer polynomials to investigate the estimates f...

Using differential subordination, we consider conditions of $\beta$ so that some multivalent analytic functions are subordinate to ${(1+z)}^{\gamma }$ ($0<\gamma \le 1$). Notably, these results are applied to derive sufficient conditions for $f\in A$ to satisfy the condition $\left|{\left(\frac{z{f}^{\prime }\left(z\right)}{}\right)}^{}\right|$...

The fractional integral is prolific in giving rise to interesting outcomes when associated with different operators. For the study presented in this paper, the fractional integral is associated with the convolution product of multiplier transformatio...

The aim of this paper is to define and explore a certain class of analytic functions involving the $(p,q)$-Wanas operator related to the Janowski functions. We discuss geometric properties, growth and distortion bounds, necessary and sufficient conditi...

It is well known that there are two important classes of analytic functions of Ma-Minda type (MMT): Ma-Minda starlike and Ma-Minda convex functions. In this work, we suggest a new class of analytic functions, which is normalized in the open unit disk...

In the current study, we provide a novel qualitative new subclass of analytical and bi-univalent functions in the symmetry domain $\mathbb{U}$ defined by the use of Gegenbauer polynomials. We derive estimates for the Fekete–Szegö functional problems...

This paper aims to provide sufficient conditions for starlikeness and convexity of Hadamard product (convolution) of certain multivalent analytic functions with positive real parts. Moreover, the starlikeness conditions for a certain integral operato...

The study on fractional integrals of confluent hypergeometric functions provides interesting subordination and superordination results and inspired the idea of using this operator to introduce a new class of analytic functions. Given the class of fun...

Let $S_l^{*}$ denote the class of analytic functions f in the open unit disk $\mathbb{D}=\{z:|z|<1\}$ normalized by $f(0)=f^{\prime }(0)-1=0$ , which is subordinate to exponential function, $\frac{z{f}^{\prime }(z)}{f(z)}$...

Using the Salagean q-differential operator, we investigate a novel subclass of analytic functions in the open unit disc, and we use the Hadamard product to provide some inclusion relations. Furthermore, the coefficient conditions, convolution propert...

The objective of the present paper is to derive certain geometric properties of analytic functions associated with the Dziok–Srivastava operator.

In this work, we derive coefficient bounds for the symmetric Toeplitz matrices $T_2\left(2\right)$, $T_2\left(3\right)$, $T_3\left(1\right)$, and $T_3\left(2\right)$, which are the known first four determinants for a new family of analytic functions with Borel distribution series in the open unit disk U....

In this article, we use the q-derivative operator and the principle of subordination to define a new subclass of analytic functions related to the q-Ruscheweyh operator. Sufficient conditions, sharp bounds for the initial coefficients, a Fekete&ndash...