New Subclass Of Bi-univalent Functions Research Articles

Coefficient Estimates for New Subclasses of Bi-Univalent Functions Associated with Jacobi Polynomials

Our research introduces new subclasses of analytical functions that are defined by Jacobi polynomials. We then proceed to estimate the Fekete-Szegö functional problem and the Maclaurin coefficients for this specific subfamily, denoted as |a2| and |a3|. Furthermore, we demonstrate several new results that emerge when we specialize the parameters used in our main findings.

Some New Applications of the Quantum Calculus for New Families of Sigmoid Activation Bi-univalent Functions Connected to Horadam Polynomials

The study of q-calculus is becoming increasingly prominent in the field of geometric function theory, reflecting a growing interest in its applications. In this research work, we first develop a new type of modified Sigmoid-Salagean q-differential operator in the open unit disk D, utilizing the concepts of quantum calculus and the Sigmoid activation function. Using this newly defined q analogous differential operator and Horadam polynomials, we introduce new subclasses of bi-univalent functions in D. We determine upper bounds on initial coefficients, as well as the Fekete-Szeg ̈o problems, for functions belonging to these special families. Additionally, we discuss several interesting consequences related to the findings presented in this study.

Coefficient Estimate Problems For A New Subclass of Bi-univalent Functions Linked with the Generalized Bivariate Fibonacci-Like Polynomial

In this article, using the definition of generalized bivariate Fibonacci-like polynomials that include Horadam and Chebyshev polynomials a novel subclass of bi-univalent functions are introduced. Then, some bounds are determined for the initial Taylor-Maclaurin coefficients of the functions belonging to this new subclass. Further, the well-known Fekete-Szeg\"{o} problem is discussed for the defined subclass. Finally, certain remarks and corollaries are indicated for the some special values of variables.

Applications of Caputo-Type Fractional Derivatives for Subclasses of Bi-Univalent Functions with Bounded Boundary Rotation

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 Taylor–Maclaurin coefficients, |a2| and |a3|. Furthermore, the famous Fekete–Szegö inequality is obtained for the newly defined subclasses of bi-univalent functions. Several consequences of our results are pointed out which are new and not yet discussed in association with bounded boundary rotation. Some improved results when compared with those already available in the literature are also stated as corollaries.

Coefficient Estimates for New Subclasses of Bi-Univalent Functions with Bounded Boundary Rotation by Using Faber Polynomial Technique

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 existing coefficient bounds in the literature.

New Subclasses of Bi-Univalent Functions Associated with Exponential Functions and Fibonacci Numbers

تمت مناقشة الفئة للدوال ثنائية أحادية التكافؤ من قبل الباحث لوين وحصل على تقدير للمعامل الثاني فيها، عرَّف ساكار و واناس فئتين فرعيتين جديدتين للدوال ثنائية أحادية التكافؤ وحصلا على الحدود العليا للمعاملات الأولية |a2| و |a3| للتوابع في هذه الفئات الفرعية، دزيوك وآخرون .قدموا الفئة من الدوال الشبيهة بالصدفة المحدبة ، والتي تشير إلى وجود اتصال بين الدالة وأرقام فيبوناتشي. في الآونة الأخيرة تم تعريف العديد من فئات الدوال ثنائية أحادية التكافؤ، استنادًا إلى مؤثرات معروفة مثل مؤثر سيلاجين، ومؤثر تريمبلي، ومؤثر تكامل كوماتو، ومؤثر الالتواء، ومؤثر العبودي التفاضلي وغيرها. يهدف هذا البحث إلى تقديم فئتين فرعيتين جديدتين من الدوال ثنائية أحادية التكافؤ باستخدام التبعية ومؤثر تكامل كوماتو والتي تتضمن الدوال الأسية والمنحنيات الشبيهة بالصدفة مع أرقام فيبوناتشي، وكذلك إيجاد تقدير للمعاملات الأولية لهذه الفئات الفرعية. تم تعريف الفئة الفرعية الأولى باستخدام التبعية لتابع المنحنى الشبيهة بالصدفة المتعلق بأرقام فيبوناتشي وتم تعريف الفئة الفرعية الثانية باستخدام التبعية للدالة الأسية. وتم استخدام مؤثر تكامل كوماتو في كل فئة من هذه الفئات الفرعية. تم الحصول على الحدود للمعاملات الأولية، وتحديداً المعاملين الثاني و الثالث لتوابع هذه الفئات الفرعية.

Study of quantum calculus for a new subclass of bi-univalent functions associated with the cardioid domain

In this article, we make use of the concepts of subordination and the q-calculus theory to analyze a new class of analytic bi-univalent functions associated to the cardioid domain. Our main focus is to derive a sharp inequality for a newly defined class of analytic and bi-univalent functions in the open unit disc U. We explore the bounds of initial coefficients, Fekete-Szegö type problems, and coefficient inequalities for newly established families. In addition, we explore some recent findings for the bi-univalent function and inverse function. Additionally, a few well-known results are mentioned to help make links between earlier and current results.

Fekete-Szegö type functionals associated with certain subclasses of bi-univalent functions

In this article, we define and discuss some new subclasses of bi-univalent functions associated with Fibonacci numbers and shell-like curves. We estimate the first two Taylor-Maclaurin coefficients for functions belonging to these classes. We study the inequalities related with Fekete-Szegö type. Furthermore, we point out some corollaries related to existing result.

"A New Subclass of Bi-Univalent Functions Associated with Balancing Polynomial"

"A New Subclass of Bi-Univalent Functions Associated with Balancing Polynomial"

Certain new subclasses of bi-univalent function associated with bounded boundary rotation involving sǎlǎgean derivative

<p>In this article, using the Sǎlǎgean operator, we introduced three new subclasses of bi-univalent functions associated with bounded boundary rotation in open unit disk $ \mathbb{E}. $ For these new classes, we first obtain initial Taylor-Maclaurin's coefficient bounds. Furthermore, the famous Fekete-Szegö inequality was also derived for these new subclass functions. Some improved results, when compared with those available in the literature, are also stated.</p>

Coefficient Bounds for a Certain Subclass of Bi-Univalent Functions Associated with Lucas-Balancing Polynomials

In this paper, we introduce a new subclass of bi-univalent functions defined using Lucas-Balancing polynomials. For functions in each of these bi-univalent function subclasses, we derive estimates for the Taylor–Maclaurin coefficients a2 and a3 and address the Fekete–Szegö functional problems for functions belonging to this new subclass. We demonstrate that several new results can be derived by specializing the parameters in our main findings. The results obtained from this study will enrich the theoretical foundation of this field and open new avenues for mathematical inquiry and application.

Fekete-Szegö Inequality for a Subclass of Bi-univalent Functions by Applying Sălăgean q-Differential Operator

Throughout this study, we propose a new subclass of bi-univalent functions by applying Sălăgean q-differential operator and denoted as LΣ_q^k (λ,ϕ). Further, we acquired the values of the initial coefficients |a_2 | and |a_3 | for functions f∈LΣ_q^k (λ,ϕ) which yield to this study’s preliminary result. Subsequently, the preliminary result was applied to obtain the upper bound of Fekete-Szegö inequality, |a_3-ρa_2^2 |, for functions f∈LΣ_q^k (λ,ϕ).

New subclasses of bi-univalent functions connected with a q-analogue of convolution based upon the Legendre polynomials

"In this paper, we introduce new subclasses of analytic and bi-univalent functions connected with a q-analogue of convolution by using the Legendre polynomials. Furthermore, we find estimates on the fi rst two Taylor-Maclaurin coef cients |a_2| and |a_2| for functions in these subclasses and obtain Fekete-Szego problem for these subclasses."

Faber polynomials estimates for bi-univalent functions of complex order involving q-derivative

<p>In this paper, we define a new subclass of bi-univalent functions of complex order which is defined by subordination in the open unit disc <em>D</em> by using operator. Furthermore, using the Faber polynomial expansions, we get upper bounds for the coefficients of function belonging to this class. It is known that the calculus without the notion of limits is called q-calculus which has influenced many scientific fields due to its important applications. The generalization of derivative in q-calculus that is q-derivative was defined and studied by Jackson. A function is said to be bi-univalent in <em>D</em> if both <em>F</em> and <em>F</em><sup>−1</sup> are univalent in <em>D</em>. The class consisting of bi-univalent functions is denoted by <em>σ</em>. The Faber polynomials play an important role in various areas of mathematical sciences, especially in geometric function theory. The purpose of our study is to obtain bounds for the general coefficients by using Faber polynomial expansion under certain conditions for analytic bi-univalent functions in subclass and also, we obtain improvements on the bounds for the first two coefficients and of functions in this subclass. In certain cases, our estimates improve some of those existing coefficient bounds.</p>

Investigating New Subclasses of Bi-Univalent Functions Associated with q-Pascal Distribution Series Using the Subordination Principle

In the real world, there are many applications that find the Pascal distribution to be a useful and relevant model. One of these is the normal distribution. In this work, we develop a new subclass of analytic bi-univalent functions by making use of the q-Pascal distribution series as a construction. These functions involve the q-Gegenbauer polynomials, and we use them to establish our new subclass. Moreover, we solve the Fekete–Szegö functional problem and analyze various different estimates of the Maclaurin coefficients for functions that belong to the new subclass.

Generalized bivariate Fibonacci polynomial and two new subclasses of bi-univalent functions

This paper deals with two new subclasses of holomorphic and bi-univalent functions in the open unit disk defined by generalized bivariate Fibonacci polynomials. In this paper the coefficient bounds are estimated for [Formula: see text] and [Formula: see text] which [Formula: see text] and [Formula: see text] are the Taylor–Maclaurin coefficients of the functions belonging to these new subclasses. Then, the Fekete–Szegö problem is handled for the functions in these subclasses. Also, several remarks are presented. The results of this paper generalize certain earlier results in the literature.

Second Hankel Determinant for a New Subclass of Bi-Univalent Functions Related to the Hohlov Operator

A new subclass of bi-univalent functions associated with the Hohlov operator is introduced. Certain properties such as the coefficient bounds, Fekete-Szegö inequality and the second Hankel determinant for functions in the subclass are obtained. In particular, several known results are generalized.

Bi-Starlike Function of Complex Order Involving Mathieu-Type Series Associated with Telephone Numbers

For the first time, we attempted to define two new sub-classes of bi-univalent functions in the open unit disc of the complex order involving Mathieu-type series, associated with generalized telephone numbers. The initial coefficients of functions in these classes were obtained. Moreover, we also determined the Fekete–Szegö inequalities for function in these and several related corollaries.

A New Comprehensive Subclass of Analytic Bi-Univalent Functions Related to Gegenbauer Polynomials

In the current study, we provide a novel qualitative new subclass of analytical and bi-univalent functions in the symmetry domain U defined by the use of Gegenbauer polynomials. We derive estimates for the Fekete–Szegö functional problems and the Taylor–Maclaurin coefficients a2 and a3 for the functions that belong to each of these new subclasses of the bi-univalent function classes. Some more results are revealed after concentrating on the parameters employed in our main results.

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.