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    Characterizations for certain subclasses of starlike and convex functions associated with generalized Dini functions
    (Springer Heidelberg, 2022) Ece, Sadettin; Eker, Sevtap Sümer
    In this paper, we investigated some sufficient conditions for the generalized Dini function which is the combination of the generalized Bessel function of first kind to be in certain subclasses of univalent functions.
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    Geometric properties of normalized Rabotnov function
    (Hacettepe Üniversitesi Fen Fakültesi, 2022) Eker, Sevtap Sümer; Ece, Sadettin
    In the present paper, our aim is to study geometric properties of normalized Rabotnov functions. For this purpose, we determined sufficient conditions for univalency, close-to- convexity, convexity and starlikeness of the normalized Rabotnov functions in the open unit disk.
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    Geometric properties of the Miller-Ross functions
    (Springer International Publishing AG, 2022) Eker, Sevtap Sümer; Ece, Sadettin
    In the present paper, our aim is to study geometric properties of normalized Miller-Ross functions. For this purpose, we determined sufficient conditions for univalency, close-to-convexity, convexity and starlikeness of the normalized Miller-Ross functions in the open unit disk.
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    Normalized dini functions connected with k-Uniformly convex and k-Starlike functions
    (Korean Soc Computational & Applied Mathematics-KSCAM, 2021) Ece, Sadettin; Eker, Sevtap Sümer; Şeker, Bilal
    The purpose of the present paper is to give sufficient conditions for normalized Dini function which is the special combination of the generalized Bessel function of first kind to be in the classes k-starlike functions and k-uniformly convex functions.
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    On strongly Ozaki bi-close-to-convex functions
    (TUBITAK, 2019) Tezelci, Münevver; Eker, Sevtap Sümer
    In this paper, we introduce and investigate a new subclass of strongly Ozaki bi-close-to-convex functions in the open unit disk. We have also found estimates for the first two Taylor-Maclaurin coefficients for functions belonging to this class. The results presented in this paper have been shown to generalize and improve the work of Brannan and Taha.
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    On subclasses of bi-convex functions defined by Tremblay fractional derivative operator
    (Babes-Bolyai University, 2019) Eker, Sevtap Sümer; Şeker, Bilal
    We introduce and investigate new subclasses of analytic and biunivalent functions defined by modified Tremblay operator in the open unit disk. Also we obtain upper bounds for the coefficients of functions belonging to these classes
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    On Subclasses Of Bi-Starlike Functions Defined By Tremblay Fractional Derivative Operator
    (Mehmet Zeki SARIKAYA, 2018) Eker, Sevtap Sümer; Şeker, Bilal
    In this paper, we introduce and investigate new subclasses of strongly bi-starlike and bi-starlike functions defined by Tremblay fractional derivative operator in the open unit disk. Also we obtain upper bounds for the coefficients $|a_{2}|$ and $|a_{3}|$ of functions belonging to these classes. Unlike recent studies, we use different technique for obtain the upper bounds on the coefficients $|a_{3}|$. Theorems proved in this paper generalizes the results given in [3].
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    The second hankel determinant of logarithmic coefficients for Strongly Ozaki close-to-convex functions
    (Springer, 2023) Eker, Sevtap Sümer; Lecko, Adam; Çekiç, Bilal; Şeker, Bilal
    The aim of this paper is to determine sharp bound for the second Hankel determinant of logarithmic coefficients H2 , 1(Ff/ 2) of strongly Ozaki close-to-convex functions in the open unit disk. Furthermore, sharp bound of H2,1(Ff-1/2) , where f- 1 is the inverse function of f, is also computed. The results show an invariance property of the second Hankel determinants of logarithmic coefficients H2 , 1(Ff/ 2) and H2,1(Ff-1/2) for strongly convex functions.
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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.