Person: BAYRAM, HASAN
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BAYRAM
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HASAN
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Publication Coefficient estimates for certain subclasses of analytic functions defined by new operator(Amer Inst Physics, 2021-01-01) Cakalli, H; Kocinac, LDR; Ashyralyev, A; Harte, R; Dik, M; Canak, I; Kandemir, HS; Tez, M; Gurtug, O; Savas, E; Akay, KU; Ucgun, FC; Uyaver, S; Ashyralyyev, C; Sezer, SA; Turkoglu, AD; Onvural, OR; Sahin, H; Bayram, Hasan; BAYRAM, HASAN; Yalcin, Sibel; YALÇIN TOKGÖZ, SİBEL; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; Cakalli, H; Kocinac, LDR; Ashyralyev, A; Harte, R; Dik, M; Canak, I; Kandemir, HS; Tez, M; Gurtug, O; Savas, E; Akay, KU; Ucgun, FC; Uyaver, S; Ashyralyyev, C; Sezer, SA; Turkoglu, AD; Onvural, OR; Sahin, H; 0000-0001-8106-6834; 0000-0002-0243-8263; B-1379-2014; AAE-9745-2020In this paper, we investigate certain subclasses of analytic functions defined by generalized differential operators involving binomial series. Also, we obtain coefficient estimates involving of the nonhomogeneous Cauchy-Euler differential equation of order r.Publication Q-analogue of a new subclass of harmonic univalent functions associated with subordination(MDPI, 2022-04-01) Bayram, Hasan; BAYRAM, HASAN; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0001-8106-6834; JAC-6018-2023In this article, we introduce and investigate the q-analogue of a new subclass of harmonic univalent functions defined by subordination. We first obtain a coefficient characterization of these functions. We give compactness and extreme points, distortion bounds, necessary and sufficient convolution conditions for this subclass of harmonic univalent functions with negative coefficients. The symmetry properties and other properties of the q-analogue subclass of functions presented in this paper shed light on future studies.Publication Bi-univalent functions based on binomial series-type convolution operator related with telephone numbers(Mdpi, 2023-10-01) Vijaya, Kaliappan; Murugusundaramoorthy, Gangadharan; Bayram, Hasan; BAYRAM, HASAN; Yalçın, Sibel; YALÇIN TOKGÖZ, SİBEL; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0001-8106-6834; 0000-0002-0243-8263; JAC-6018-2023; AAE-9745-2020This paper introduces two novel subclasses of the function class sigma for bi-univalent functions, leveraging generalized telephone numbers and Binomial series through convolution. The exploration is conducted within the domain of the open unit disk. We delve into the analysis of initial Taylor-Maclaurin coefficients |a2| and |a3|, deriving insights and findings for functions belonging to these new subclasses. Additionally, Fekete-Szego inequalities are established for these functions. Furthermore, the study unveils a range of new subclasses of sigma, some of which are special cases, yet have not been previously explored in conjunction with telephone numbers. These subclasses emerge as a result of hybrid-type convolution operators. Concluding from our results, we present several corollaries, which stand as fresh contributions in the domain of involution numbers involving hybrid-type convolution operators.Publication Some properties of certain multivalent harmonic functions(MDPI, 2023-05-23) Oros, Georgia Irina; Yalçın, Sibel; Bayram, Hasan; YALÇIN TOKGÖZ, SİBEL; BAYRAM, HASAN; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-0243-8263; 0000-0001-8106-6834; AAE-9745-2020; JAC-6018-2023In this paper, various features of a new class of normalized multivalent harmonic functions in the open unit disk are analyzed, including bounds on coefficients, growth estimations, starlikeness and convexity radii. It is further demonstrated that this class is closed when its members are convoluted. It can also be seen that various previously introduced and investigated classes of multivalent harmonic functions appear as special cases for this class.Publication Certain properties of harmonic functions defined by a second-order differential inequality(Mdpi, 2023-10-01) Breaz, Daniel; Cotirla, Luminita-Ioana; Yalçın, Sibel; YALÇIN TOKGÖZ, SİBEL; Durmus, Abdullah; Bayram, Hasan; BAYRAM, HASAN; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-0095-1346; 0000-0002-0243-8263; AAE-9745-2020; JAC-6018-2023The Theory of Complex Functions has been studied by many scientists and its application area has become a very wide subject. Harmonic functions play a crucial role in various fields of mathematics, physics, engineering, and other scientific disciplines. Of course, the main reason for maintaining this popularity is that it has an interdisciplinary field of application. This makes this subject important not only for those who work in pure mathematics, but also in fields with a deep-rooted history, such as engineering, physics, and software development. In this study, we will examine a subclass of Harmonic functions in the Theory of Geometric Functions. We will give some definitions necessary for this. Then, we will define a new subclass of complex-valued harmonic functions, and their coefficient relations, growth estimates, radius of univalency, radius of starlikeness and radius of convexity of this class are investigated. In addition, it is shown that this class is closed under convolution of its members.