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Öğe Applications of fractional derivatives for Alexander integral operator(Springer Heidelberg, 2021) Guney, Hatun Ozlem; Acu, Mugur; Breaz, Daniel; Owa, ShigeyoshiLet T-n be the class of functions f (z) = z + a(n+1)z(n+1) + a(n+2)z(n+2) +... that are analytic in the closed unit disc U. With m different boundary points z(s), (s = 1, 2,..., m), we consider alpha(m) is an element of e(i beta) A(j+lambda) f (U), here A(j+lambda) is given by using fractional derivatives Dj+lambda f (z) for f (z) is an element of T-n. Using A(j+lambda), we introduce a subclass P-n(alpha(m), beta, rho; j, lambda) of T-n. The main goal of our paper is to discuss some interesting results of f (z) in the class P-n(alpha(m), beta, rho; j, lambda).Öğe INTEGRAL PROPERTIES OF SOME FAMILIES OF MULTIVALENT FUNCTIONS WITH COMPLEX ORDER(Univ Babes-Bolyai, 2009) Guney, H. Ozlem; Breaz, DanielIn the present paper, we study integral properties of two families of p-valently analytic functions of complex order defined of the derivative operator of order m. The obtained results improve known results.Öğe A New Operator for Meromorphic Functions(Mdpi, 2022) Guney, Hatun Ozlem; Breaz, Daniel; Owa, ShigeyoshiLet S be the class of functions f ( z) of the form f ( z) = 1/z + Sigma(infinity)(k =0)a(k)z(k), which are analytic in the punctured disk. Using the differentiations and integrations, new operator D-n f (z) is introduced for f (z) is an element of Sigma. The object of the present paper is to discuss some interesting properties for D-n f (z) and some properties concerned with different boundary points of the open unit disk. Moreover, some simple examples for our results are shown.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 some interesting classes of analytic functions related to univalent functions(Mdpi, 2024) Güney, Hatun Özlem; Breaz, Daniel; Owa, Shigeyoshi; 0000-0002-3010-7795; 0000-0002-0095-1346Let A over bar be the new general class of functions f(z) of the form f(z) = z + Sigma(infinity)(k=1)a(1+k/2)z(1+k/2) that are analytic in the open unit disc U. In the present paper, for f(z) is an element of A over bar , we consider classes S*(alpha), C (alpha) and R(alpha) and obtain some interesting properties of f(z) is an element of A over bar concerning S*(alpha), C (alpha) and R(alpha), applying subordinations of f(z).Öğe On the univalence criterion of a general integral operator(Springer, 2008) Breaz, Daniel; Guney, H. OzlemIn this paper we considered an general integral operator and three classes of univalent functions for which the second order derivative is equal to zero. By imposing supplimentary conditions for these functions we proved some univalent conditions for the considered general operator. Also some interesting particullar results are presented. Copyright (c) 2008 D. Breaz and H. Ozlem Guney. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Öğe Some properties for subordinations of analytic functions(MDPI, 2023) Güney, Hatun Özlem; Breaz, Daniel; Owa, ShigeyoshiLet the class of functions of (Formula presented.) of the form (Formula presented.), which are denoted by (Formula presented.) and called analytic functions in the open-unit disk. There are many interesting properties of the functions (Formula presented.) in the class (Formula presented.) concerning the subordinations. Applying the three lemmas for (Formula presented.) provided by Miller and Mocanu and by Nunokawa, we consider many interesting properties of (Formula presented.) with subordinations. Furthermore, we provide simple examples for our results. We think it is very important to consider examples of the results.Öğe Starlike Functions of the Miller-Ross-Type Poisson Distribution in the Janowski Domain(Mdpi, 2024) Murugusundaramoorthy, Gangadharan; Gueney, Hatun oezlem; Breaz, DanielIn this paper, considering the various important applications of Miller-Ross functions in the fields of applied sciences, we introduced a new class of analytic functions f, utilizing the concept of Miller-Ross functions in the region of the Janowski domain. Furthermore, we obtained initial coefficients of Taylor series expansion of f, coefficient inequalities for f-1 and the Fekete-Szego problem. We also covered some key geometric properties for functions f in this newly formed class, such as the necessary and sufficient condition, convex combination, sequential subordination and partial sum findings.Öğe Upper bounds of the third hankel determinant for bi-univalent functions in crescent-shaped domains(Multidisciplinary Digital Publishing Institute (MDPI), 2024) Shakir, Qasim Ali; Tayyah, Adel Salim; Breaz, Daniel; Cotîrlă, Luminita-Ioana; Rapeanu, Eleonora; Sakar, Fethiye MügeThis paper investigates the third Hankel determinant, denoted (Formula presented.), for functions within the subclass (Formula presented.) of bi-univalent functions associated with crescent-shaped regions (Formula presented.). The primary aim of this study is to establish upper bounds for (Formula presented.). By analyzing functions within this specific geometric context, we derive precise constraints on the determinant, thereby enhancing our understanding of its behavior. Our results and examples provide valuable insights into the properties of bi-univalent functions in crescent-shaped domains and contribute to the broader theory of analytic functions. © 2024 by the authors.Öğe The yamaguchi–noshiro type of bi-univalent functions connected with the linear q-convolution operator(Multidisciplinary Digital Publishing Institute (MDPI), 2023) Breaz, Daniel; El-Deeb, Sheza M.; Aydoǧan, Seher Melike; Sakar, Fethiye MügeIn the present paper, the authors introduce and investigate two new subclasses of the function class (Formula presented.) of bi-univalent analytic functions in an open unit disk (Formula presented.) connected with a linear q-convolution operator. The bounds on the coefficients (Formula presented.) and (Formula presented.) for the functions in these new subclasses of (Formula presented.) are obtained. Relevant connections of the results presented here with those obtained in earlier work are also pointed out.
