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Subordination Properties of bi-univalent functions Involving Horadam Polynomials

JOURNAL OF FUNCTION SPACES 2025年第1期2025卷

作者： Amini, Ebrahim Al-Omari, Shrideh Payame Noor Univ Dept Math Tehran Iran Al Balqa Appl Univ Fac Sci Dept Math Salt Jordan

In this research, we investigate a family of q-extensions defined on an open unit disk, which is based on bi-univalent functions associated with differential subordination. Next, we define certain classes of bi-univalent functions using generalized Horadam polynomials. For the functions in the recently defined classes, estimates of a few coefficients are also given. Furthermore, we obtain the Fekte-Szego inequality for functions in the specified classes and give good instances of the described new sets utilizing the Nephroid function. Further findings are also investigated.

关键词： analytic functions bi-univalent functions coefficient bounds Fekte-Szego inequality Horadam polynomials nephroid function q-derivative operator

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An application of the Mittag-Leffler-type Borel distribution and Gegenbauer polynomials on a certain subclass of bi-univalent functions

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HELIYON 2024年第10期10卷 e31469页

作者： Hussen, Abdulmtalb Navajo Tech Univ Sch Engn Math & Technol Lowerpoint Rd State Hwy 371 Crownpoint NM 87313 USA

The Mittag-Leffler-type Borel distribution is widely recognized and utilized as a beneficial and pertinent model across numerous applications. This study presents a new subclass of normalized analytic bi-univalent functions that combines Gegenbauer polynomials and the Mittag-Leffler-type Borel distribution. Employing this subclass enables us to derive novel approximations for TaylorMaclaurin coefficients, | a 2 | and | a 3 |, as well as delve into the investigation of the Fekete-Szeg & ouml;functional. Additionally, we explore a variety of new findings that arise through the specialization of parameters in our primary results.

关键词： Borel distribution Mittag-Leffler Gegenbauer polynomials bi-univalent functions Analytic functions Fekete-Szeg & ouml problem

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The Miller-Ross Poisson distribution and its applications to certain classes of bi-univalent functions related to Horadam polynomials

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HELIYON 2024年第7期10卷 e28302页

作者： Alnajar, Omar Ogilat, Osama Amourah, Ala Darus, Maslina Alatawi, Maryam Salem Univ Kebangsaan Malaysia Fac Sci & Technol Dept Math Sci Bangi 43600 Malaysia Al Ahliyya Amman Univ Fac Arts & Sci Dept Basic Sci Amman 19328 Jordan Sohar Univ Fac Educ & Arts Math Educ Program Sohar 3111 Oman Univ Tabuk Fac Sci Dept Math Tabuk 71491 Saudi Arabia

Within the scope of this research, we introduce a novel category of bi-univalent functions. Horadam polynomials are utilized to characterize these functions by utilizing series from the Poisson distribution of the Miller -Ross type. functions from these new categories have been used to construct estimates for the Fekete-Szego functional, as well as estimates of the Taylor -Maclaurin coefficients |1 2 | and |1 3 |. These projections were created for the methods in each of these brandnew subclasses. We made some additional discoveries after, focusing on the traits that contributed to our initial findings.

关键词： Poisson distribution series Horadam polynomials bi-univalent functions Analytic functions Fekete-Szeg & ouml problem

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The study of coefficient estimates and Fekete-Szego inequalities for the new classes of m-fold symmetric bi-univalent functions defined using an operator

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2023年第1期2023卷 1-13页

作者： Breaz, Daniel Cotirla, Luminita-Ioana 1 Decembrie 1918 Univ Alba Iulia Dept Math Alba Iulia Romania Tech Univ Cluj Napoca Dept Math Cluj Napoca Romania

The objective of this paper is to introduce new classes of m-fold symmetric bi-univalent functions. We discuss estimates on the Taylor-Maclaurin coefficients |a(m+1)| and |a(2m+1)|, and the Fekete-Szego problem is also considered for the new classes of functions introduced. We denote these classes by MF - S-Sigma,m(p,q)(h), MF - S-Sigma,m(p,q)(s), and MF -S-Sigma,m(b,d). Quantum calculus aspects are also considered in this study to enhance its novelty and to obtain more interesting results.

关键词： Analytic functions bi-univalent functions Fekete-Szego functional m-fold symmetric Coefficient estimates Coefficient bounds

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Estimating Coefficient Bounds for Classes of bi-univalent functions Defined by Fractional Derivatives 8th

Estimating Coefficient Bounds for Classes of Bi-univalent Fu...

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8th International Arab Conference on Mathematics and Computations

作者： Al-Refai, Oqlah Zarqa Univ Fac Sci Dept Math Zarqa Jordan

ISBN: (纸本)9789819748785;9789819748761;9789819748754

Let f (z) = z + Sigma(infinity)(k=n) a(k) z(k);(n >= 2) be a bi-univalent function in the unit disk U = {z : |z| < 1}). We investigate bounds of |a(n)|, |a(2n-1)|, |a(2n-1) - na(n)(2)| and |a(2n-1) - a(n)(2)| for classes of bi-univalent functions defined by fractional derivatives. The results include generalizations and improvements for well known estimates.

关键词： univalent functions bi-univalent functions Fractional derivatives Faber polynomials Coefficient estimates

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bi-univalent functions ASSOCIATED WITH INVOLUTION NUMBERS BASED ON SALAGEAN-ERDELY-KOBER OPERATOR

JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS

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JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS 2025年 2025卷

作者： Vijaya, Kaliyappan Murugusundaramoorthy, Gangadharan Al-Sa'di, Sa'ud Vellore Inst Technol Sch Adv Sci Vellore 632014 India Kuwait Univ Coll Sci Dept Math Safat 13060 Kuwait

In this paper, we propose two new subclasses of bi-univalent functions defined in the open unit disk and denoted by Omega, and relate them to the concept of generalized telephone numbers. These subclasses utilize the Salagean-Erdely-Kober operator. Furthermore, we examine the initial TaylorMaclaurin coefficients |a(2)| and |a(3)| and derived Fekete-Szego inequalities for the functions that belongs to these new subclasses. Additionally, we introduce several other new subclasses of Omega based on SalageanErdely-Kober operator, which have not been previously explored in connection with telephone numbers. Some corollaries are also presented.

关键词： . Analytic functions bi-univalent functions Coefficient bounds Fractional-order derivative univalent functions

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Exploring Fekete-Szegő inequalities for an admissible class of bi-univalent functions involved Gegenbauer polynomials

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Arab Journal of Basic and Applied Sciences 2025年第1期32卷 51-56页

作者： Al-Sa’di, Sa’ud Ahmad, Ibrar Sakar, Muge Hussain, Saqib Noor, Saima Department of Mathematics Faculty of Science The Hashemite University Zarqa 13133 Jordan Department of Mathematics COMSATS University Islamabad Abbottabad Campus 22060 Pakistan Department of Business Administration Dicle University Diyarbakır Turkey Department of Basic Sciences Preparatory Year Deanship King Faisal University Al Ahsa 31982 Saudi Arabia

This paper presents a newly defined subclass of bi-univalent functions linked to the Genenbauer polynomial. The functions in this subclass satisfy specific subordination conditions within a symmetric domain inside the open unit disk. For this subclass, we derive bounds for the Taylor-Maclaurin coefficients (Formula presented.) (Formula presented.) and the Fekete-Szegő functional (Formula presented.) The existing method has been extended to produce additional bi-univalent subfamilies as well as other special functionalities. © 2025 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.

关键词： Analytic functions bi-univalent functions Fekete-Szegő problem Gegenbauer polynomial subordination

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COEFFICIENTS BOUNDS FOR A SUBCLASS OF bi-univalent functions DEFINED BY AL-OBOUDI DIFFERENTIAL OPERATOR

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THERMAL SCIENCE 2022年第Spe2期26卷 S583-S589页

作者： Uyanik, Neslihan Ozdemir, Burcin Gokkurt Anadolu Univ Fac Educ Dept Math & Sci Educ Eskisehir Turkey Bartin Univ Fac Educ Dept Math & Sci Educ Bartin Turkey

In this paper, we investigate a new subclass Sigma(n)(delta)(lambda,gamma,phi) of analytic and biunivalent functions in the open unit disk u = {z: |z|<1} defined by Al-Oboudi differential operator. We obtain coefficient bounds | a(2) | and |a(3) |for functions belonging to subclass Sigma(n)(delta)(lambda,gamma,phi). Relevant connections of the results presented here with various well-known results are briefly indicated.

关键词： analytic functions univalent functions bi-univalent functions subordination Al-Oboudi differential operator

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The second Hankel determinant for subclasses of bi-univalent functions associated with a nephroid domain

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REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS 2022年第4期116卷 1-21页

作者： Srivastava, Hari Mohan Murugusundaramoorthy, Gangadharan Bulboaca, Teodor Univ Victoria Dept Math & Stat Victoria BC V8W 3R4 Canada China Med Univ China Med Univ Hosp Dept Med Res Taichung 40402 Taiwan Azerbaijan Univ Dept Math & Informat 71 Jeyhun Hajibeyli St Baku AZ1007 Azerbaijan Int Telemat Univ Uninettuno Sect Math I-100186 Rome Italy VIT Univ Sch Adv Sci Vellore 632014 Tamil Nadu India Babes Bolyai Univ Fac Math & Comp Sci R-400084 Cluj Napoca Romania

In the present paper, we obtain the estimates for the first two initial Taylor-Maclaurin coefficients and for the upper bounds of the Fekete-Szego functional for new subclasses of the class Sigma of normalized analytic and bi-univalent functions, which are defined here with the aid of the Nephroid function. We also determine upper bounds of the functional vertical bar a(2)a(4) - a(3)(2)vertical bar for the functions that belong to these classes. A related open problem as well some potential directions for further researches are posed in the concluding section.

关键词： Analytic and univalent functions Starlike and convex functions bi-univalent functions Strongly bi-starlike functions Coefficient bounds Subordination Fekete-Szego inequalities Hankel determinant

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Initial estimates for certain subclasses of bi-univalent functions with ?\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa $$\end{document}-Fibonacci numbers

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AFRIKA MATEMATIKA 2023年第3期34卷 1-21页

作者： Magesh, Nanjundan Nirmala, Jodalli Yamini, Jagadeesan Swamy, Sondekola Rudra Govt Arts Coll Men Postgrad & Res Dept Math Krishnagiri 635001 Tamilnadu India Maharanis Sci Coll Women Dept Math Bangalore 5600001 Karnataka India Govt First Grade Coll Vijayanagar Dept Math Bangalore 560104 Karnataka India RV Coll Engn Dept Comp Sci & Engn Bangalore 560059 Karnataka India

Initial estimates for certain subclasses of bi-univalent functions with K-Fibonacci numbers

关键词： univalent functions bi-univalent functions ?-Fibonacci numbers Shell-like function Convex shell-like function Pseudo starlike function Bazilevic function

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