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    Applications laguerre polynomials for families of bi-univalent functions defined with (p,q)-wanas operator
    (Multidisciplinary Digital Publishing Institute (MDPI), 2023) Wanas, Abbas Kareem; Sakar, Fethiye Müge; Lupaş, Alina Alb
    In current manuscript, using Laguerre polynomials and (Formula presented.) -Wanas operator, we identify upper bounds (Formula presented.) and (Formula presented.) which are first two Taylor-Maclaurin coefficients for a specific bi-univalent functions classes (Formula presented.) and (Formula presented.) which cover the convex and starlike functions. Also, we discuss Fekete-Szegö type inequality for defined class.
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    Coefficient bounds and Fekete–Szegö Inequality for a new family of bi-univalent functions defined by Horadam polynomials
    (Springer Science and Business Media Deutschland GmbH, 2022) Wanas, Abbas Kareem; Güney, Hatun Özlem
    In the current article, we introduce and investigate a new family KΣ(δ, λ, x) of analytic and bi-univalent functions by using the Horadam polynomials defined in the open unit disk U. We determine upper bounds for the initial Taylor–Maclaurin coefficients. Further we obtain the Fekete–Szegö inequality of functions belonging to this family. We also point out several certain special cases for our results.
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    New Families of Bi-univalent Functions Associated with the Bazilevic Functions and the ?-Pseudo-Starlike Functions
    (Springer Int Publ Ag, 2021) Srivastava, H. M.; Wanas, Abbas Kareem; Guney, H. Ozlem
    In this article, we define two new families T-Sigma(mu, gamma, lambda; alpha) and T-Sigma*(mu, gamma, lambda; beta) of normalized holomorphic and bi-univalent functions which involve the Bazilevic. functions and the lambda-pseudo-starlike functions. For functions in each of these families, we establish the bounds for vertical bar a(2)vertical bar and vertical bar a(3)vertical bar, where a(2) and a(3) are the initial Taylor-Maclaurin coefficients. We also point out several special cases and consequences of our results.
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    On a fekete–szegö problem associated with generalized telephone numbers
    (Multidisciplinary Digital Publishing Institute (MDPI), 2023) Breaz, Daniel; Wanas, Abbas Kareem; Sakar, Fethiye Müge; Aydoǧan, Seher Melike
    One of the important problems regarding coefficients of analytical functions (i.e., Fekete–Szegö inequality) was raised by Fekete and Szegö in 1933. The results of this research are dedicated to determine upper coefficient estimates and the Fekete–Szegö problem in the class (Formula presented.), which is defined by generalized telephone numbers. We also indicate some specific conditions and consequences of results found by us.
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    Some m-fold symmetric bi-univalent function classes and their associated Taylor-Maclaurin coefficient bounds
    (Springer Nature, 2024) Srivastava, Hari Mohan; Sabır, Pishtiwan Othman; Eker, Sevtap Sümer; Wanas, Abbas Kareem; Mohammed, Pshtiwan Othman; Chorfi, Nejmeddine; Baleanu, Dumitru
    The Ruscheweyh derivative operator is used in this paper to introduce and investigate interesting general subclasses of the function class ?m of m-fold symmetric bi-univalent analytic functions. Estimates of the initial Taylor-Maclaurin coefficients |am+1| and |a2m+1| are obtained for functions of the subclasses introduced in this study, and the consequences of the results are discussed. Additionally, the Fekete-Szegö inequalities for these classes are investigated. The results presented could generalize and improve some recent and earlier works. In some cases, our estimates are better than the existing coefficient bounds. Furthermore, within the engineering domain, the utilization of the Ruscheweyh derivative operator can encompass a broad spectrum of engineering applications, including the robotic manipulation control, optimizing optical systems, antenna array signal processing, image compression, and control system filter design. It emphasizes the potential for innovative solutions that can significantly enhance the reliability and effectiveness of engineering applications.
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    Toeplitz determinants for a certain family of analytic functions endowed with borel distribution
    (MDPI, 2023) Wanas, Abbas Kareem; Sakar, Fethiye Müge; Oros, Georgia Irina; Cotîrlă, Luminiţa-Ioana
    In this work, we derive coefficient bounds for the symmetric Toeplitz matrices (Formula presented.), (Formula presented.), (Formula presented.), and (Formula presented.), which are the known first four determinants for a new family of analytic functions with Borel distribution series in the open unit disk U. Further, some special cases of results obtained are also pointed.