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Öğe Analytic functions related with q-conic domain and associated with a convolution operator(Korean Society for Computational and Applied Mathematics, 2023) Frasin, Basem Aref; Amourah, Ala; Shah, Syed Ghoos Ali; Hussain, Saqib; Khan, Shahbaz; Sakar, Fethiye MügeIn this paper, we defined some new classes of analytic functions in conic domains. We investigate some important properties such as necessary and sufficient conditions, coefficient estimates, convolution results, linear combination, weighted mean, arithmetic mean, radii of starlikeness and distortion for functions in these classes. It is important to mentioned that our results are generalization of number of existing results in the literature.Öğe Application of Gegenbauer polynomials for biunivalent functions defined by subordination(Scientific Technical Research Council Turkey-TUBITAK, 2022) Sakar, Fethiye Müge; Hussain, Saqib; Ahmad, IbrarWe present and investigate a new subclass of biunivalent functions by applying Gegenbouer polynomials in this paper. Also, we find nonsharp estimates on the first two coefficients vertical bar b(0)vertical bar and vertical bar b(1)vertical bar for functions belonging to this subclass. Furthermore, the Fekete-Szego inequality vertical bar b(1) - eta b(0)(2)vertical bar for this subclass is obtained. We also point out some consequences of results.Öğe 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 AlbIn 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.Öğe A certain subclass of bi-univalent analytic functions introduced by means of the q -analogue of Noor integral operator and Horadam polynomials(TUBITAK, 2019) Akgül, Arzu; Sakar, Fethiye MügeIn the present study, by using the Horadam Polnomials and q-analogue of Noor integral oprerator, we target to construct an interesting connection between the geometric function theory and that of special functions. Also, by defining a new class of bi-univalent analytic functions, we investigate coefficient estimates and famous Fekete-Szegö inequality for functions belonging to this interesting classÖğe Classes of harmonic functions related to mittag-leffler function(Multidisciplinary Digital Publishing Institute (MDPI), 2023) Al-Dohiman, Abeer A.; Frasin, Basem Aref; Taşar, Naci; Sakar, Fethiye MügeThe purpose of this paper is to find new inclusion relations of the harmonic class (Formula presented.) with the subclasses (Formula presented.) (Formula presented.) and (Formula presented.) of harmonic functions by applying the convolution operator (Formula presented.) associated with the Mittag-Leffler function. Further for (Formula presented.), several special cases of the main results are also obtained.Öğe Coefficient bounds for a new subclass of analytic bi-close-to-convex functions by making use of Faber polynomial expansion(TUBITAK, 2017) Sakar, Fethiye Müge; Güney, Hatun ÖzlemRecently, in the literature, we can see quite a few papers about general coefficient bounds for subclasses of bi-univalent functions. However, we can find just a few papers about general coefficient estimates for subclasses of bi-close-to-convex functions. In the present study, we give and look into a new subclass of analytic and bi-close-to-convex functions in the open unit disk. Making use of the Faber series, we have an upper bound for the general coefficient of functions in this class. We also demonstrate the invisible behavior of the beginning coefficients of a special subclass of bi-close-to-convex functions.Öğe Coefficient Bounds for a Subclass of $m$-fold Symmetric Bi-univalent Functions Involving Hadamard Product and Differential Operator(Murat TOSUN, 2019) Sakar, Fethiye Müge; Aydoğan, Seher Melike; Altınkaya, ŞahseneIn this study, we construct a new subclass of $m$-fold symmetric bi-univalent functions using by Hadamard product and generalized Salagean differential operator in the open unit disk $U=\left\{ z\in \mathbb{C} :\left\vert z\right\vert <1\right\} $. We establish upper bounds for the coefficients $\left\vert a_{m+1}\right\vert $ and $\left\vert a_{2m+1}\right\vert $ belonging to this new class. The results presented here generalize some of the earlier studies.Öğe Coefficient estimation utilizing the faber polynomial for a subfamily of bi-univalent functions(MDPI, 2023) Alsoboh, Abdullah; Amourah, Ala; Sakar, Fethiye Müge; Ogilat, Osama; Gharib, Gharib Mousa; Zomot, NasserThe paper introduces a new family of analytic bi-univalent functions that are injective and possess analytic inverses, by employing a q-analogue of the derivative operator. Moreover, the article establishes the upper bounds of the Taylor–Maclaurin coefficients of these functions, which can aid in approximating the accuracy of approximations using a finite number of terms. The upper bounds are obtained by approximating analytic functions using Faber polynomial expansions. These bounds apply to both the initial few coefficients and all coefficients in the series, making them general and early, respectively.Öğe Çok kriterli karar verme yöntemlerinden TOPSIS yöntemi ile fakültelerin akademik performanslarının analizi(Dicle Üniversitesi İktisadi ve İdari Bilimler Fakültesi, 2023) Yıldırım, Zafer; Sakar, Fethiye MügeBu çalışmada akademik performans seviyelerini de belirleyen akademik teşvik sistemi genel olarak incelenmiş ve buna yönelik geliştirici yönlerin neler olduğu tespit edilmeye çalışılmıştır. Akademik teşvik açısından yapılan performans analizinde Dicle Üniversitesi’nde faaliyette bulunan fakültelere ait 2019, 2020 ve 2021 yıllarına ait veriler üç dönem halinde ayrı ayrı analiz edilmiştir. Performans analizi için önceden belirlenmiş kriterler ENTROPI yöntemi ile ağırlıklandırılmış ve daha sonra çok kriterli karar verme metotlarından olan TOPSIS yöntemi ile fakülteler üç dönem içinde değerlendirilmiştir. Analiz sonucunda 2019 yılı için Tıp Fakültesi birinci, Eğitim Fakültesi ikinci ve Hukuk Fakültesi üçüncü olmuştur. 2020 yılı için Tıp Fakültesi birinci, Eğitim Fakültesi ikinci ve Ziraat Fakültesi üçüncü olmuştur. Son olarak 2021 yılı için Tıp Fakültesi birinci, Eğitim Fakültesi ikinci ve Fen Fakültesi üçüncü olmuştur.Öğe Connections between various subclasses of planar harmonic mappings involving Mittag-Leffler functions(Springer Heidelberg, 2024) Taşar, Naci; Sakar, Fethiye Müge; Frasin, Basem ArefIn this existing paper, we examine a connection between certain class of harmonic univalent functions with starlike and convex harmonic functions define in the open unit disk by applying the convolution operator defined by Mittag-Leffler function. Several corollaries and consequences of the main results are also obtained.Öğe Differential subordinations in harmonic mappings(Springer Science and Business Media Deutschland GmbH, 2021) Aydoğan, Melike; Bshouty, Daoud; Miller, Sanford S.; Sakar, Fethiye Müge; 0000-0002-4822-9571; 0000-0002-3884-3957Differential subordination of analytic functions proved to be useful in many applications. The book of Miller and Mocanu ((2000) Differential Subordinations. In Theory and applications, monographs and textbooks in pure and applied mathematics, vol 225. Marcel Dekker Inc, New York) sums up most of the advancement in the field and the references to the date of its publication. The theory of harmonic mappings can benefit from this theory. We attempt to discuss some aspects of this generalization.Öğe Exploring subordination and argument behavior in a new class of analytic functions(Wiley, 2025) Göksel, İzzet; Bekçi, Zeynep; Aydoğan, Seher Melike; Sakar, Fethiye MügeThe class Ap includes functions with a specific starting term and higher-order terms in their series, and studying these functions involves examining their analytic properties, argument behavior, and subordination characteristics, which lead to various interesting and significant results in complex analysis. The functions within Ap are designed to explore properties that arise from their structure and the way their series are constructed, and the main interest in this class lies in analyzing how these functions behave in various mathematical contexts, particularly in relation to argument shifts and the relationships between different functions. In a nutshell, the class Ap offers a framework for examining a specific type of analytic function with a structured series expansion, thereby allowing for a deeper investigation into their mathematical properties and applications. The new class Ap, which is related to the class Ap, is characterized by functions that are analytic in the open unit disk and have a specific series expansion involving fractional powers. The object of this paper is to discuss some interesting applications of f(z)is an element of Ap concerning argument problems and subordinations, and furthermore, prominent examples for the main results are given.Öğe Genelleştirilmiş diferansiyel operatörler kullanılarak tanımlanmış meromorfik harmonik fonksiyonların bazı alt sınıfları(2015) Sakar, Fethiye MügeBu çalışma beş bölümden oluşmaktadır. İlk bölümde, analitik ve harmonik yalınkat fonksiyonların gelişimi hakkında bilgi verilmiştir. İkinci bölümde çalışma boyunca ihtiyaç duyulan temel kavram, tanım ve teoremlerden söz edilmiş, ayrıca yalınkat fonksiyonlar ve bazı alt sınıflarından bahsedilmiştir. Üçüncü bölümde harmonik fonksiyonlar ve harmonik fonksiyonlar ile ilgili temel kavram, tanım ve teoremler verilmiş, ayrıca harmonik yalınkat fonksiyonların bazı alt sınıfları ve subordinasyon kavramından bahsedilmiştir. Dördüncü bölümde, birim diskin dışı olan ? U zz ?? : 1? ? bölgesinde, yeni genelleştirilmiş bir diferansiyel operatör yardımıyla tanımlanan harmonik meromorfik yıldızıl fonksiyonların yeni sınıfları verilmiştir. Ayrıca bu sınıflar için katsayı eşitsizlikleri, büyüme sınırları ve ekstrem noktaları elde edilmiştir. Beşinci bölümde, birim diskin dışı olan ? U zz ?? : 1? ? bölgesinde, yeni genelleştirilmiş bir Al-Oboudi diferansiyel operatörünün yardımıyla tanımlanan çok değerli harmonik meromorfik ve yön koruyan fonksiyonların yeni bir sınıfı verilmiştir. Ayrıca bu sınıf için katsayı sınırları, büyüme sınırları, ekstrem noktaları ve konveks birleşim özelliği belirlenmişir. Anahtar Kelimeler: Analitik, Harmonik yalınkat fonksiyonlar, Meromorfik fonksiyonlar, Al-Oboudi diferansiyel operatörü, Katsayı eşitsizlikleri, Ekstrem noktalarÖğe Hadamard çarpım ile tanımlı k-düzgün çokdeğerli harmonik fonksiyonların yeni bir sınıfı(2015) Sakar, Fethiye MügeBu çalışma iki bölümden oluşmaktadır. Birinci bölümde, diğer bölümlerde kullanılacak olan temel tanım ve teoremler verildi. Ayrıca bu bölümde birim diskte analitik fonksiyonlar olmak üzere şeklinde normalize edilmiş, yön koruyan harmonik yalınkat tipindeki fonksiyonların sınıfı ve bunun alt sınıflarının temel özellikleri incelendi. İkinci bölümde, çokdeğerli harmonik fonksiyonların sınıfının ve ile adlandırılan yeni iki özel alt sınıfı çalışıldı. Ayrıca bu sınıflar ile ilgili Katsayı Kestirimleri, Büyüme sınırları, extreme noktaları ve Kapalılık özellikleri ayrıntılı bir şekilde incelendi.Öğe New classes of harmonic functions defined by fractional operator(Isik University, 2018) Sakar, Fethiye Müge; Bağcı, Yasemin; Güney, Hatun ÖzlemIn the present study, we introduce an investigation of new subclasses of harmonic functions which are defined by fractional operator. Firstly, using by fractional operator, we define new subclasses of harmonic functions. Later, we obtain main theorems of our study which contain sufficient and necessary coefficient bounds for functions related to the classes newly defined. Also, several particular characterization properties of these classes are given. Some of these properties involve extreme points, convex combination, distortion bounds. Finally, several corollaries of the main theorems are presented.Öğe A new general integral operator(Hikari Ltd., 2016) Güney, Hatun Özlem; Sakar, Fethiye Müge; Bulut, SerapIn this paper, we define a new general integral operator for certain analytic and p-valent functions in the unit disc U. Using this integral operator, we obtain many known integral operators.Öğe A novel fractional structure of a multi-order quantum multi-integro-differential problem(Springer Science and Business Media Deutschland GmbH, 2020) Duc Phuong, Nguyen; Sakar, Fethiye Müge; Etemad, Sina; Rezapour, ShahramIn the present research manuscript, we formulate a new generalized structure of the nonlinear Caputo fractional quantum multi-integro-differential equation in which such a multi-order structure of quantum integrals is considered for the first time. In fact, in the light of this type of boundary value problem equipped with the multi-integro-differential setting, one can simply study different cases of the existing usual integro-differential problems in the literature. In this direction, we utilize well-known analytical techniques to derive desired criteria which guarantee the existence of solutions for the proposed multi-order quantum multi-integro-differential problem. Further, some numerical examples are considered to examine our theoretical and analytical findings using the proposed methods.Öğe 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 MelikeOne 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.Öğe On Sense of Yamakawa family of meromorphic bi-univalent and bi-sub ordinate functions(Tübitak, 2021) Sakar, Fethiye MügeAbstract: This study offers three different univalent function families of bi-meromorphic and bi-subordinate functions defined on ∆ = {z : z ∈ C, 1 < |z| < ∞}. The estimations of the first three coefficients |b0|, |b1|, |b2| and extra |b0b1 + 2b2| are obtained for the functions of these families. We also point out some closely related cases for our results.Öğe On The Fekete-Szegö Problem for Generalized Class M? ?? Defined By Differential Operator(2016) Sakar, Fethiye Müge; Aytaş, Sultan; Güney, Hatun ÖzlemBuçalışmada,Fekete-Szegöproblemiçalışılmıştır. 2 3 2 3 f z z az az ( ) .... ?? ? ? Uz z ?? ? ? C : 1? , açık birim diskinde normalize edilmiş analitik fonksiyonların bir sınıfı olsun. ? ? 1 koşulu altında ? tipli ? mertebeli * , ( ) S? ? ? sınıfı ile ilgili, 2 a a 3 2 ? ? içinkesinmaksimumdeğerieldeedilmiştir.
