Subfamily Of Functions Research Articles

Some Inclusion Properties for Hohlov Operator to be in Comprehensive Subfamilies of Analytic functions

Some Inclusion Properties for Hohlov Operator to be in Comprehensive Subfamilies of Analytic functions

The sharp bound of the third Hankel determinant for certain subfamilies of analytic functions

The sharp bound of the third Hankel determinant for certain subfamilies of analytic functions

Closed 𝑘-Schur Katalan functions as 𝐾-homology Schubert representatives of the affine Grassmannian

Recently, Blasiak–Morse–Seelinger introduced symmetric func- tions called Katalan functions, and proved that the K K -theoretic k k -Schur functions due to Lam–Schilling–Shimozono form a subfamily of the Katalan functions. They conjectured that another subfamily of Katalan functions called closed k k -Schur Katalan functions is identified with the Schubert structure sheaves in the K K -homology of the affine Grassmannian. Our main result is a proof of this conjecture. We also study a K K -theoretic Peterson isomorphism that Ikeda, Iwao, and Maeno constructed, in a nongeometric manner, based on the unipotent solution of the relativistic Toda lattice of Ruijsenaars. We prove that the map sends a Schubert class of the quantum K K -theory ring of the flag variety to a closed K K - k k -Schur Katalan function up to an explicit factor related to a translation element with respect to an antidominant coroot. In fact, we prove this map coincides with a map whose existence was conjectured by Lam, Li, Mihalcea, Shimozono, and proved by Kato, and more recently by Chow and Leung.

The Fekete–Szegö inequality for a subfamily of q-analogue analytic functions associated with the modified q-Opoola operator

In the current work, we alter the Opoola derivative operator using quantum calculus. We examine a novel specific subfamily of analytical functions with complex order connected to the subordination principal by using the modified [Formula: see text]-Opoola derivative operator. Next, we examine the Fekete–Szegö inequality for the generated subclass in the open unit disk. This paper sheds light the significant connections between the results introduced in this work and previous results.

Notes on some classes of spirallike functions associated with the $q$-integral operator

The object of the present paper is to find the essential properties for certain subfamilies of analytic and spirallike functions which are generated by $q$-integral operator. Further, we derive membership relations for functions belong to these subfamilies, and also we determine coefficient estimates.

Two Inclusive Subfamilies of bi-univalent Functions

The aim of this article is to establish two new and qualitative subfamilies F(ε, κ, ℵ) and G(ε, κ, ℵ) of biunivalent functions. For functions in these subfamilies, we determine the first two Maclaurin coefficient estimations |C2| and |C3|, and address the Fekete–Szeg¨o problem. Additionally, we mention some corollaries related to the main results.

Some Analysis of the Coefficient-Related Problems for Functions of Bounded Turning Associated with a Symmetric Image Domain

In the last few years, numerous subfamilies of univalent functions, whether directly or indirectly associated with exponential functions, have been introduced and thoroughly investigated. Among these, the families Se*, Ce and Re defined by subordination to ez have been intensively investigated. While the coefficient problem on the class Se* and Ce has been solved in many cases, in this paper, we mainly intend to compute the sharp estimates of some initial coefficients, the Feketo–Szegö inequality, and the sharp bounds of second- and third-order Hankel determinants for functions belonging to the class Re. This work has the potential to significantly enrich and enhance the exploration of univalent functions in conjunction with exponential functions, making the field more comprehensive and robust.

Applications of First-Order Differential Subordination for Subfamilies of Analytic Functions Related to Symmetric Image Domains

This paper presents a geometric approach to the problems in differential subordination theory. The necessary conditions for a function to be in various subfamilies of the class of starlike functions and the class of Carathéodory functions are studied, respectively. Further, several consequences of the findings are derived.

Zalcman Functional and Majorization Results for Certain Subfamilies of Holomorphic Functions

In this paper, we investigate sharp coefficient functionals, like initial four sharp coefficient bounds, sharp Fekete–Szegö functionals, and, for n=1 and 2, sharp Zalcman functionals are evaluated for class of functions associated with tangent functions. Furthermore, we provide some majorization results for some non-vanishing holomorphic functions, whose ratios are related to various domains in the open unit disk.

Sharp coefficient estimates for $\vartheta$-spirallike functions involving generalized q-integral operator

The aim of this article is to identify a new subfamily of spirallike functions and then to demonstrate necessary and sufficient conditions, sharp coefficients estimates for functions in this subfamily.

Estimate of third Hankel determinant for a subfamily of analytic functions

Abstract In this article, our aim is to study analytic functions related with Salagean operator and associated with the right half of the lemniscate of Bernoulli. We find the estimates of the third Hankel determinant for new family of analytic functions. It is important to mention that our results generalize a number of existence results in the literature.

Norm Estimates of the Pre-Schwarzian Derivatives for Functions with Conic-like Domains

The pre-Schwarzianand Schwarzian derivatives of analytic functions f are defined in U, where U is the open unit disk. The pre-Schwarzian as well as Schwarzian derivatives are popular tools for studying the geometric properties of analytic mappings. These can also be used to obtain either necessary or sufficient conditions for the univalence of a function f. Because of the computational difficulty, the pre-Schwarzian norm has received more attention than the Schwarzian norm. It has applications in the theory of hypergeometric functions, conformal mappings, Teichmüller spaces, and univalent functions. In this paper, we find sharp norm estimates of the pre-Schwarzian derivatives of certain subfamilies of analytic functions involving some conic-like image domains. These results may also be extended to the families of strongly starlike, convex, as well as to functions with symmetric and conjugate symmetric points.

The sharp bound for the third Hankel determinant of the inverse of functions associated with lemniscate of Bernoulli

We present the sharp bounds for the third Hankel determinant [Formula: see text] and Zalcman functional [Formula: see text] of the inverse function of the familiar subfamily of starlike functions associated with the right half of lemniscate of Bernoulli.

Applications of Gegenbauer Polynomials for Subfamilies of Bi-Univalent Functions Involving a Borel Distribution-Type Mittag-Leffler Function

In this research, a novel linear operator involving the Borel distribution and Mittag-Leffler functions is introduced using Hadamard products or convolutions. This operator is utilized to develop new subfamilies of bi-univalent functions via the principle of subordination with Gegenbauer orthogonal polynomials. The investigation also focuses on the estimation of the coefficients |aℓ|(ℓ=2,3) and the Fekete–Szegö inequality for functions belonging to these subfamilies of bi-univalent functions. Several corollaries and implications of the findings are discussed. Overall, this study presents a new approach for constructing bi-univalent functions and provides valuable insights for further research in this area.

On a Subfamily of q-Starlike Functions with Respect to m-Symmetric Points Associated with the q-Janowski Function

The main objective of this paper is to study a new family of analytic functions that are q-starlike with respect to m-symmetrical points and subordinate to the q-Janowski function. We investigate inclusion results, sufficient conditions, coefficients estimates, bounds for Fekete–Szego functional |a3−μa22| and convolution properties for the functions belonging to this new class. Several consequences of main results are also obtained.

Third Hankel Determinant for a Subfamily of Holomorphic Functions Related with Lemniscate of Bernoulli

The main goal of this investigation is to obtain sharp upper bounds for Fekete-Szegö functional and the third Hankel determinant for a certain subclass SL∗u,v,α of holomorphic functions defined by the Carlson-Shaffer operator in the unit disk. Finally, for some special values of parameters, several corollaries were presented.

Computation of Conditional Expectations with Guarantees

Theoretically, the conditional expectation of a square-integrable random variable Y given a d-dimensional random vector X can be obtained by minimizing the mean squared distance between Y and f(X) over all Borel measurable functions f :mathbb {R}^d rightarrow mathbb {R}. However, in many applications this minimization problem cannot be solved exactly, and instead, a numerical method which computes an approximate minimum over a suitable subfamily of Borel functions has to be used. The quality of the result depends on the adequacy of the subfamily and the performance of the numerical method. In this paper, we derive an expected value representation of the minimal mean squared distance which in many applications can efficiently be approximated with a standard Monte Carlo average. This enables us to provide guarantees for the accuracy of any numerical approximation of a given conditional expectation. We illustrate the method by assessing the quality of approximate conditional expectations obtained by linear, polynomial and neural network regression in different concrete examples.

On a subfamily of starlike functions related to hyperbolic cosine function

We introduce and study a new Ma–Minda subclass of starlike functions $${\mathcal {S}}^*_{\varrho },$$ defined as $$\begin{aligned} {\mathcal {S}}^{*}_{\varrho }:=\left\{ f\in {\mathcal {A}}:\frac{zf'(z)}{f(z)} \prec \cosh \sqrt{z}=:\varrho (z), z\in {\mathbb {D}} \right\} , \end{aligned}$$ associated with an analytic univalent function $$\cosh \sqrt{z},$$ where we choose the branch of the square root function so that $$\cosh \sqrt{z}=1+z/2!+z^{2}/{4!}+\cdots .$$ We establish certain inclusion relations for $${\mathcal {S}}^{*}_{\varrho }$$ and deduce sharp $${\mathcal {S}}^{*}_{\varrho }$$ -radii for certain subclasses of analytic functions.

A New Subclass of Bi-Univalent Functions Defined by a Certain Integral Operator

We introduce a comprehensive subfamily of analytic and bi-univalent functions in this study using Horadam polynomials and the q-analog of the Noor integral operator. We establish upper bounds for the absolute values of the second and the third coefficients and the Fekete–Szegö functional for the functions belonging to this family. Various observations of the results presented here are also discussed.

Problems concerning sharp coefficient functionals of bounded turning functions

<abstract><p>The work presented in this article has been motivated by the recent research going on the Hankel determinant bounds and their related consequences, as well as the techniques used previously by many different authors. We aim to establish a new subfamily of holomorphic functions connected with the hyperbolic tangent function with bounded boundary rotation. We investigate the sharp estimate of the third Hankel determinant for this newly defined family of functions. Moreover, for the defined functions family, the Krushkal inequality, the first four initial sharp bounds of the logarithmic coefficients and the sharp second Hankel determinant of the logarithmic coefficients are given.</p></abstract>