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Öğe An analytical investigatıon on starlikeness and convexity properties for hypergeometric functions(2020) Yıldız, İsmet; Akyar, AlaattinIn this study, we analytically investigate hypergeometric functions having some properties such as convexityand starlike. We fundamentally focus on obtaining desired conditions on the parameters a, b , and c in order that ahypergeometric function to be in various subclasses of starlike and convex functions of order $\alpha\;=\;2^{-r}$and order $\alpha\;=\;2^{-r}$type $\beta\;=\;2^{-1}$, with r is a positive integer.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 Hipergeometrik fonksiyonların starlike (yıldızıl) ve konveks olması için yeterlilik şartları üzerine(Düzce Üniversitesi, 2021) Akyar, Alaattin; Yıldız, İsmetBu tezde, hipergeometrik ve ilgili fonksiyonların starlike ve konveks olması incelenmiştir. Özellikle zF(a;b; c; z) Gauss hipergeometrik fonksiyonunun r bir pozitif tamsayı olmak üzere 2^(-r) dereceden starlike ve konveks fonksiyonlarının sınıflarında olması için a;b;c parametreleri üzerindeki koşulları verilmiştir.Tez yedi bölümden oluşmaktadır. Yapılan tezin bölüm bazında kısa bir açıklaması aşağıdaki gibidir: İlk bölüm, kısa bir literatür taramasıyla giriş için ayrılmıştır. İkinci bölümde, tek değişkenli kompleks fonksiyonlarla ilgili temel tanım ve teoremler verilmiştir. Üçüncü bölüm, analitik ve univalent fonksiyon teorisinin temel tanım ve teoremleri ile ilgili olup ayrıca bu bölümde univalent fonksiyonların temel özellikleri ve univalent fonksiyonların altsınıfları verilmiştir. Dördüncü bölümde, hipergeometrik fonksiyonlar ve ilgili tanımlar, teoremler ve ilgili fonksiyonlar verildi. Beşinci bölüm tezin ana kısmı olup, bu bölümde zF(a;b; c; z) Gauss hipergeometrik fonksiyonunun r bir pozitif tamsayı olmak üzere 2^(-r) dereceden starlike ve konveks fonksiyonlarının sınıflarında olması için a;b;c parametreleri üzerindeki koşulları sağlayan teoremler ve ispatları verilmiştir. Son olarak altıncı bölüm, elde edilen sonuçlar ve tavsiyeler içindir.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 A new subclass of certain analytic univalent functions associated with hypergeometric functions(Scientific Technical Research Council Turkey-Tubitak, 2021) Akyar, AlaattinThe main objective of the present paper is to give with using the linear operator theory and also hypergeometric representations of related functions a new special subclass TSp(2(-r), 2(-1)), r is an element of Z(+) of uniformly convex functions and in addition a suitable subclass of starlike functions with negative Taylor coefficients. Furthermore, the provided trailblazer outcomes in presented study are generalized to certain functions classes with fixed finitely many Taylor coefficients.Öğe ON SUFFICIENT CONDITION FOR STARLIKENESS OF CONFLUENT HYPERGEOMETRIC FUNCTIONS(Yildiz Technical Univ, 2018) Yıldız, İsmet; Akyar, Alaattin; Mert, OyaIn the present paper, firstly some univalent functions are obtained as special cases of hypergeometric functions and then we have discussed the starlikeness of confluent hypergeometric functions.Öğe ON SUFFICIENT CONDITIONS FOR CLOSE-TO-CONVEXITY OF ORDER 2(-r)(Yildiz Technical Univ, 2018) Yıldız, İsmet; Akyar, Alaattin; Mert, OyaThe main idea of the present paper is to obtain sufficient conditions for close-to-convexity of order in 2(-r), where r is a positive integer.Öğe On the Analytical Determination of Geometric Characterizations of Analytic Functions(2023) Akyar, AlaattinAs it is known, there are many sufficient conditions for the classification complex functions of one variable f(z), which are analytic and univalent in the open unit disc U = {z ? C ? SzS < 1}, and are also normalized with f(0) = 1 ? f?(0) = 0 which are also known as normalization conditions. In this sense, the main goal of present article is to derive some special sufficient conditions for f(z) to be starlike of order 2?r and convex of order 2?r in U , with r is a positive integer.Öğe On the Sufficient Conditions for the Univalence of Definite Integral Operators Involving Certain Functions in S Class(Mustafa UÇKUN, 2025) Akyar, AlaattinIn general terms, integral operators play a very important role as a useful mathematical tool in order to reach the desired results and make different inferences by analyzing the relevant issues in mathematics and applied sciences. It is important to understand the conditions under which integral operators map certain analytic functions to starlike and convex functions and effectively characterizing and using them is of great importance for studies in this field. In present article, some integral operators preserving class S are examined from a different perspective and the relevant inequalities and equations for their univalence are determined and solved.Öğe Some Results on Important Inequalities for Univalent Functions with Positive and Negative Coefficients(Düzce Üniversitesi, 2023) Akyar, AlaattinAs it is known from Real Analysis, inequalities are used to give the definition of many mathematical concepts formally and to analyze them analytically. Similarly, the geometric characterizations of the range of analytic and univalent functions in the open unit disc U = {z ? C :
