250 Results Found

In this article, the authors use the Faber polynomial expansions to find the general coefficient estimates for a few new subclasses of bi-univalent functions with bounded boundary rotation and bounded radius rotation. Some of the results improve the...

Recently, a number of features and properties of interest for a range of bi-univalent and univalent analytic functions have been explored through systematic study, e.g., coefficient inequalities and coefficient bounds. This study examines ${\mathcal{S}}_q^{\mathrm{\&d}}$...

In the current article, we introduce several new subclasses of m-fold symmetric analytic and bi-univalent functions associated with bounded boundary and bounded radius rotation within the open unit disk $\mathbb{D}.$ Utilizing the Faber polynomial expansion, we...

In this research article, we introduce a new subclass of concave bi-univalent functions associated with bounded boundary rotation defined on an open unit disk. For this new class, we make an attempt to find the first two initial coefficient bounds. I...

The objective of the present article is to introduce new subclasses of bi-Bazilevič functions, bi-quasi-convex functions and $\alpha$-exponentially bi-convex functions involving functions with bounded boundary rotation of order $\nu$. For the abov...

In this article, for the first time by using Caputo-type fractional derivatives, we introduce three new subclasses of bi-univalent functions associated with bounded boundary rotation in an open unit disk to obtain non-sharp estimates of the first two...

The study explores analytic, geometric and algebaraic properties of two subclasses of analytic functions: the class of Bounded Radius Rotation denoted by ${\mathcal{R}}_{\mathfrak{s}}{,}_{\varrho }(\mathcal{A},\mathcal{B},z)$, and the class of Bounded Boundary Rotation denoted by ${\mathcal{V}}_{\mathfrak{s}}{,}_{\varrho }(\mathcal{A},\mathcal{B},z)$, both...

The results presented in this paper deal with the classical but still prevalent problem of introducing new classes of m-fold symmetric bi-univalent functions and studying properties related to coefficient estimates. Quantum calculus aspects are also...

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...

In the current article, we introduce a new class of bi-close-to-convex functions with bounded boundary rotation. For this new class, the authors obtain the first three initial coefficient bounds of the newly defined bi-close-to-convex functions with...

In this article, through the application of the q-Sălăgean operator associated with functions characterized by bounded boundary rotation, we propose a few new subclasses of bi-univalent functions that utilize the q-Sălăgean operat...

Let $\mathcal{B}{T}_{4l}$ denote a subclass of bounded turning functions connected with a four-leaf-type domain. The goal of the study is to probe into the bounds of coefficients $|b_6|,|b_7|,|b_8|$, the bounds of the logarithmic coefficients, and the third-order determin...

Let ${\mathcal{C}}_0\left(h\right)$ be a subclass of analytic and close-to-convex functions defined in the open unit disk by the formula $\mathrm{R}\mathrm{e}\{(1-z^2)f^{\prime }\left(z\right)\}>0$. In this paper, some coefficient problems for ${\mathcal{C}}_0\left(h\right)$ are considered. Some properties and bounds of several...

The concept of coefficient estimates on univalent functions is one of the interesting aspects explored recently by many researchers. Motivated by this direction, in this present work, we obtain the upper bounds of initial inverse coefficients and log...

In numerous geometric and physical applications of complex analysis, estimating the sharp bounds of coefficient-related problems of univalent functions is very important due to the fact that these coefficients describe the core inherent properties of...

In this paper, we discuss two well-known coefficient functionals $a_2{a}_4-{a_3}^2$ and $a_4-a_2{a}_3$ . The first one is called the Hankel determinant of order 2. The second one is a special case of Zalcman fun...

In the present paper, we aimed to discuss certain coefficient-related problems for the inverse functions associated with a bounded turning functions class subordinated with the exponential function. We calculated the bounds of some initial coefficien...

This research investigates the second Hankel determinant for a specific class of functions associated with the Daehee polynomial. To achieve this, we introduce new subclasses of starlike functions in the context of Daehee polynomials. In complex anal...

In our present investigation, some coefficient functionals for a subclass relating to starlike functions connected with three-leaf mappings were considered. Sharp coefficient estimates for the first four initial coefficients of the functions of this...

In this paper, we create a new subclass of convex functions given with tangent functions applying the combination of Babalola operators and Binomial series. Moreover, we obtain several important geometric results, including sharp coefficient bounds,...

In our present study, two subclasses of starlike functions which are symmetric about the origin are considered. These two classes are defined with the use of the sigmoid function and the trigonometric function, respectively. We estimate the first fou...

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...

Let ${\mathcal{R}}_{LP}$ denote a newly introduced subclass of bounded turning functions. The primary aim of this study is to investigate the sharp bounds of the coefficients of $|d_2|,|d_3|,|d_4|,|d_5|$, as well as to establish precise estimates for the second- and third-...

One of the challenging tasks in the study of function theory is how to obtain sharp estimates of coefficients that appear in the Taylor–Maclaurin series of analytic univalent functions, and for obtaining these bounds, researchers used the conce...

In this paper, some coefficient problems for starlike analytic functions with respect to symmetric points are considered. Bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to f...

The logarithmic functions have been used in a verity of areas of mathematics and other sciences. As far as we know, no one has used the coefficients of logarithmic functions to determine the bounds for the third Hankel determinant. In our present inv...

This paper presents a significant extension of perturbation theory techniques for estimating the roots of polynomials. Building upon foundational results and recent work by Pakdemirli and Yurtsever, as well as taking inspiration from the concept of p...

In this paper, we investigate a new family of normalized analytic functions and bi-univalent functions associated with the Srivastava–Attiya operator. We use the Faber polynomial expansion to estimate the bounds for the general coefficients $|a_n$...

This study establishes explicit Berry–Esseen bounds for residual kernel density estimators in AR(1) models with $\alpha$-mixing errors. Since the true innovations are unobservable, we introduce a residual-based estimator ${\widehat{f}}_n\left(x\right)$ and establish its...

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...

This paper considers methods of estimating a static correlated random coefficient model with panel data. We mainly focus on comparing two approaches of estimating unconditional mean of the coefficients for the correlated random coefficients models, t...

In this research article, we introduce new family ${\mathcal{R}}_G$ of holomorphic functions, which is related to the generalized bounded turning and generating functions of Gregory coefficients. Leveraging the concept of functions with positive real parts, we acqu...

In this paper, we make use of the concept of $q-$calculus in the theory of univalent functions, to obtain the bounds for certain coefficient functional problems of Janowski type starlike functions and to find the Fekete–Szegö functiona...

The purpose of this article is to obtain the sharp estimates of the first four initial logarithmic coefficients for the class ${\mathcal{BT}}_s$ of bounded turning functions associated with a petal-shaped domain. Further, we investigate the sharp estimate of Fekete...

Regression models for continuous outcomes frequently require a transformation of the outcome, which is often specified a priori or estimated from a parametric family. Cumulative probability models (CPMs) nonparametrically estimate the transformation...

Starlike and convex functions have gained increased prominence in both academic literature and practical applications over the past decade. Concurrently, logarithmic coefficients play a pivotal role in estimating diverse properties within the realm o...

We look at estimates for the Green’s function of time-fractional evolution equations of the form $D_{0+\ast }^{\nu }u=Lu$ , where $D_{0+\ast }^{\nu }$ is a Caputo-type time-fractional derivative, depending on a Lév...

Using the Lebedev–Milin inequalities, bounds on the logarithmic coefficients of an analytic function can be transferred to estimates on coefficients of the function itself and related functions. From this fact, the study of logarithmic-related...

In this paper, we first prove the q-version of Schwarz Pick’s lemma. This result improved the one presented earlier in the literature without proof. Using this novel result, we study the majorization problem for the q-general class of functions...

The logarithmic coefficients play an important role for different estimates in the theory of univalent functions. Due to the significance of the recent studies about the logarithmic coefficients, the problem of obtaining the sharp bounds for the modu...

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,...

In the present investigation, we introduce a new subclass of univalent functions $\mathcal{F}(u,\lambda )$ and a subclass of bi-univalent function ${\mathcal{F}}_{o,\mathrm{\Sigma }}(u,\lambda )$ with bounded boundary and bounded radius rotation. Some examples of the functions belonging...

In this study, we introduce the new subclasses, ${\mathcal{M}}_{\alpha }(sin)$ and ${\mathcal{M}}_{\alpha }(cos)$, of $\alpha$-convex functions associated with sine and cosine functions. First, we obtain the initial coefficient bounds for the first five coefficients of the functions t...

In this paper, we intorduce a family of analytic functions in the open unit disk which is bi-univalent. By the virtue of the Faber polynomial expansions, the estimation of $n-th$$(n\ge 3)$ Taylor–Maclaurin coefficients $\left|a_n\right|$ is obtained. Furthermore, the bound...

In this study, the generalized $(p,q)$-derivative operator is used to define a novel class of bi-univalent functions. For this class, we define constraints on the coefficients up to $|{\ell }_5|$. The functions are analyzed using a suitable operational method,...

In this note, we consider a subclass ${\mathcal{H}}_{3/2}\left(p\right)$ of starlike functions f with $f^{″}\left(0\right)=p$ for a prescribed $p\in [0,2]$. Usually, in the study of univalent functions, estimates on the Taylor coefficients, Fekete–Szegö functional or Hankel de...

One of the most important problems in the study of geometric function theory is knowing how to obtain the sharp bounds of the coefficients that appear in the Taylor–Maclaurin series of univalent functions. In the present investigation, our aim is to...

In this work, the bounds for the logarithmic coefficients ${\gamma }_n$ of the general classes ${\mathcal{S}}^{*}\left(\phi \right)$ and $\mathcal{K}\left(\phi \right)$ were estimated. It is worthwhile mentioning that the given bounds would generalize some of the previo...

The main focus of this research is to solve certain coefficient-related problems for analytic functions that are subordinated to a unique trigonometric function. For the class ${\mathcal{S}}_{sin}^{*}$, with the quantity $\frac{z{f}^{\prime }\left(z\right)}{f\left(z\right)}$ subordinated to $1+sinz$, we obtain an e...

In this paper, we are interested in the rate of convergence for the central limit theorem of the maximum likelihood estimator of the drift coefficient for a stochastic partial differential equation based on continuous time observations of the Fourier...