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Öğe AN INVESTIGATION ON GEOMETRIC PROPERTIES OF ANALYTIC FUNCTIONS WITH POSITIVE AND NEGATIVE COEFFICIENTS EXPRESSED BY HYPERGEOMETRIC FUNCTIONS(Honam Mathematical Soc, 2022) Akyar, Alaattin; Mert, Oya; Yıldız, İsmetThis paper aims to investigate characterizations on parameters k(1), k(2), k(3), k(4), k(5), l(1), l(2), l(3), and l(4) to find relation between the class of H(k, l, m, n, o) hypergeometric functions defined by F-5(4) [(l1, l2, l3, l4) (k1, k2, k3, k4, k5,) : z] = Sigma(infinity)(n=2) (k(1))(n) (k(2))(n) (k(3))(n) (k(4))(n) (k(5))(n)/(l(1))(n) (l(2))(n) (l(3))(n) (l(4))(n) (1)(n) z(n). We need to find k, l, m and n that lead to the necessary and sufficient condition for the function zF([W]), G = z(2 - F ([W])) and H-1[W] =z(2) d/dz (ln(z) - h(z)) to be in S*(2(-r)), r is a positive integer in the open unit disc D = {z : vertical bar z vertical bar < 1, z is an element of C} with h(z) = Sigma(infinity)(n=0) (k)(n)(l)(n)(m)(n)(n)(n) (1 + k/2)(n)/(k/2)(n)(1 + k - l)(n) (1 + k - m)(n) (1 + k - n)(n)n(1)(n) z(n) and [W] = [(k/2, 1 + k -l, 1 + k - m, 1 + k - n) (k, 1 + k/2, l,) (m, n) :z].Öğe Convex and Starlike Functions Defined on the Subclass of the Class of the Univalent Functions S with Order 2(- r)(Univ Maragheh, 2022) Yıldız, İsmet; Mert, Oya; Akyar, AlaattinIn this paper, some conditions have been improved so that the function g(z) is defined as g(z) = 1+ Sigma(infinity)(k >= 2) alpha n+k(zn+k), which is analytic in unit disk U, can be in more specific subclasses of the S class, which is the most fundamental type of univalent function. It is analyzed some characteristics of starlike and convex functions of order 2(-r).Öğe Examination of Resistive Switching Energy of Some Nonlinear Dopant Drift Memristor Models(Soc Microelectronics, Electron Components Materials-Midem, 2024) Tan, Rabia Korkmaz; Mert, Oya; Mutlu, ResatIn the literature, there are memristor models based on nonlinear drift mechanisms and window functions. Memristors can be employed to model resistive memories. When the resistance of a memristor undergoes a transition from its lowest value to its highest value, or vice versa, this phenomenon is referred to as resistive or memristive switching. The energy required for this transition holds particular importance, especially in the context of resistive computer memory and digital logic applications. Experimental measurements can be used to determine the resistive switching energy, and it should also be possible to calculate it theoretically based on the parameters of the memristor model utilized. Recently, the resistive switching times of some of the nonlinear dopant drift memristor models have been examined analytically considering especially their memory and digital circuit applications. In the literature, to the best of our knowledge, the resistive switching energy of the nonlinear dopant drift memristor models has not been calculated and examined in detail. In this study, the memristive switching energy of some of the well-known memristor models using a window function is calculated and found to be infinite. This is not feasible according to the experiments in which a finite resistive switching energy is consumed. The criterion that a memristor must have a finite resistive energy is also presented in this study. The results and the criterion for the resistive switching energy presented in this paper can be utilized to build more realistic memristor models in the future.Öğe FUNCTIONAL AND MATRIX APPROXIMATION OF NUMERICAL SOLUTION OF HAAR WAVELET(Publ House Bulgarian Acad Sci, 2024) Mert, Oya; Bakir, YaseminIn this article, a uniform Haar wavelet approach is devised to numerically solve the differential equations. The uniform Haar wavelet coefficients are generated by employing collocation points. The generalized approach for function and matrix approximation using Haar wavelets is proposed. This study aims to decide which method is more useful by reflecting on the differences between the two methods. Also, the application of Haar wavelets to the solution of a first and second-order ODE is described in this research. To assess its applicability and efficiency, two test problems are used. The findings obtained are compared to those obtained using the function and matrix approximation methods. For numerically solving first and second-order ODEs, the Haar wavelet methodology gives a more reliable and exact method. By estimating error norms for various problems, the performance and accuracy of the method have been shown.Öğe Mittag-Leffler Fonksiyonu ile Tanımlı Analitik Fonksiyonlar için Konvolüsyon Özellikleri(2021) Çetinkaya, Asena; Mert, OyaSon zamanlarda, Mittag-Leffler fonksiyonu yalınkat fonksiyonlar ile ilgili çalışmalarda önemli rol oynamaktadır. Bu makalede, yapılan son çalışmaların ışığında$\mathfrak q$ ?Mittag-Leffler fonksiyonu ile tanımlı yalınkat fonksiyonların iki yeni alt sınıfı tanımlanmıştır. Bu sınıflar için konvolüsyon koşulları ve katsayı tahminleri araştırılmıştır. Elde edilen bulgular literatürde olan bulgularla karşılaştırılarak sunulmuştur.Öğe Mittag-Leffler fonksiyonunu içeren analitik fonksiyonların bazı özellikleri(2021) Çetinkaya, Asena; Mert, OyaMittag-Leffler fonksiyonu 1903 yılında İsveçli matematikçi Magnus Gustav Mittag-Leffler tarafından tanımlanmıştır.Daha sonra, araştırmacılar farklı parametreler ilave ederek bu fonksiyonu genelleştirmiştir. 2015 yılında, Bansal vePrajabat, Mittag-Leffler fonksiyonunu normalize etmiş ve bu fonksiyonun açık birim diskte yalınkatlık, yıldızıllık,konvekslik ve konvekse yakınlık gibi belirli geometrik özelliklere sahip olduğunu gösteren yeterli koşullar elde etmiştir.Bu araştırma makalesinden sonra, Mittag-Leffler fonksiyonu yalınkat fonksiyonlar teorisi çalışmalarında popülerolmuştur. Bu güncel çalışmada, ????,???(??, ??, ??) ile gösterilen Mittag-Leffler fonksiyonunu içeren analitik fonksiyonlarınyeni bir sınıfı tanımlanmıştır. Ayrıca, bu fonksiyon sınıfının negatif katsayıları içeren bir alt sınıfı da tanımlanmıştır. Bufonksiyon sınıfı için katsayı tahminleri, büyüme ve distorsiyon teoremleri elde edilmiştir. Bununla birlikte, bu sınıf içinintegral eşitsizlikleri de elde edilmiştir. Ayrıca parametrelerin özel değerleri için, bu makalede tanımlanan sınıfların,araştırmacılar tarafından tanımlanan bazı fonksiyon sınıflarına indirgendiği sonucuna varılmıştır.Öğe ON COMPARISON OF SOLUTION OF ORDINARY DIFFERENTIAL EQUATION WITH HAAR WAVELET METHOD AND THE MODIFIED ISHIKAWA ITERATION METHOD(Editura Bibliotheca-Bibliotheca Publ House, 2022) Bakır, Yasemin; Mert, Oya; Orhan, ÖzlemIn this study, we have used a newly modified Ishikawa iteration method and the Haar wavelet method to solve an ordinary linear differential equation with initial conditions. Using the modified Ishikawa iteration approach, we derive approximate solutions to the issue as well as the related iterative schemes. For this problem, the Ishikawa Iteration Method is applied for different lambda and gamma values and approximation solutions for these values are compared with the approximate solution of Haar wavelet collocation and its exact solution. Finally, the error tables are written and the graphs are shown.Öğe On solution of ordinary differential equations by using HWCM, ADM and RK4(World Scientific Publ Co Pte Ltd, 2022) Bakır, Yasemin; Mert, OyaThe Haar wavelet collocation approach (HWCM) is an impressive numerical method for solving linear initial value problems when compared to the existing numerical methods (Adomian decomposition method (ADM) & Runge-Kutta method (RK4)). The objective of this study is to use the Haar-wavelet technique, Adomian decomposition technique (ADM) and Runge-Kutta (RK4) method to achieve the numerical solution of second-order ordinary differential equations. The proposed methods are applied to three different problems and the numerical results show that the HWCM has better agreement with analytic solutions than the other numerical methods.Öğe Salagean-type harmonic multivalent functions defined by q-difference operator(Univ Babes-Bolyai, 2022) Ahuja, Om P.; Çetinkaya, Asena; Mert, OyaWe introduce a new subclass of Salagean-type harmonic multivalent functions by using q-difference operator. We investigate sufficient coefficient es-timates, distortion bounds, extreme points, convolution properties and neighbor-hood for the functions belonging to this function class.Öğe SOME CONDITIONS ON STARLIKE AND CLOSE TO CONVEX FUNCTIONS(Vinca Inst Nuclear Sci, 2022) Yıldız, İsmet; Şahin, Hasan; Mert, OyaMany mathematical concepts are explained when viewed through complex function theory. We are here basically concerned with the form f(z) = a(0) + a(1)z + a(2)z(2) +.... f(z) is an element of A, f(z) = z + Sigma(infinity)(n=2)a(n)z(n) will be an analytic function in the open unit disc U = {z : |z| < 1,z is an element of C} normalized by f(0) = 0, f '(0) = 1. In this work, starlike functions and close-to-convex functions with order 1/4 have been studied according to the exact analytic requirements.Öğe Turán Type Inequalities For the (p,k)-Generalization of the Mittag-Leffler Function(Springer, 2024) Çetinkaya, Asena; Altınkaya, Şahsene; Mert, OyaThe Turán type inequalities attract attention in a variety of research fields such as orthogonal polynomials and special functions. Using the newly established (p, k)-generalization of the Mittag-Leffler function, we derive new Turán type inequalities. These outcomes are the generalization of several findings in the literature. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.
