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Öğe An application of salagean operator concerning starlike functions(MDPI, 2022) Güney, Hatun Özlem; Oros, Georgia Irina; Owa, ShigeyoshiAs an application of the well-known Salagean differential operator, a new operator is introduced and, using this, a new class of functions S-n(alpha) is defined, which has the classes of starlike and convex functions of order alpha as special cases. Original results related to the newly defined class are obtained using the renowned Jack-Miller-Mocanu lemma. A relevant example is given regarding the applications of a new proven result concerning interesting properties of class S-n (alpha).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 Fractional calculus and some properties of k-uniform convex functions with negative coefficients(Mathematical Soc Rep China, 2006) Gueney, H. Ozlem; Eker, S. Sumer; Owa, ShigeyoshiIn this paper, we introduce a class of functions (k, A, B, alpha) - UCV which is convex in the unit disk. We give some results for the class (k, A, B, alpha) - UCV, integral operators and radius of k-uniform convexity. Further, the proofs of distortion theorems for fractional calculus for functions (k, A, B, alpha) - UCV is given.Öğe GENERALIZATIONS OF THE ALEXANDER INTEGRAL OPERATOR FOR ANALYTIC MULTIVALENT FUNCTIONS(Yarmouk Univ, Deanship Research & Graduate Studies, 2022) Guney, H. Ozlem; Owa, ShigeyoshiLet T-p,T-n be a subclass of analytic multivalent functions of the form f(z) = z(p) + alpha(p) +n(zp+n) + alpha(p) +n+1 z (p+n+1) +... for every z in the open unit disc U. Applying the fractional calculus (fractional integral and fractional derivative), A (lambda)(p,n) f (z) and A(p,n)(lambda) f(z) which are generalizations of the Alexander integral operator are introduced. The object of present paper is to discuss some interesting properties of A(p,n)(-lambda) f (z) and A(p,n)(-lambda)f (z). Also, some simple examples of results for A-(lambda)(p,n) f(z) and A(p,n)(lambda)f (z) are shown. To give some simple examples is very important for the research of mathematics.Öğe Generalized operator for Alexander integral operator(Sciendo, 2020) Güney, Hatun Özlem; Owa, ShigeyoshiLetTnbe the class of functionsfwhich are defined by apower seriesf(z) =z+an+1zn+1+an+2zn+2+...for everyzin the closed unit discU.Withmdifferent boundary pointszs,(s=1,2,...,m),we considerαm∈eiβA−j−λf(U),hereA−j−λis thegeneralized Alexander integral operator andUis the open unit disc. Ap-plyingA−j−λ,a subclassBn(αm,β,ρ;j,λ)ofTnis defined with fractionalintegral for functionsf.The object of present paper is to consider someinteresting properties offto be inBn(αm,β,ρ;j,λ)Öğe Integral means inequalities for fractional derivatives of a unified subclass of prestarlike functions with negative coefficients(Springeropen, 2007) Guney, H. Ozlem; Owa, ShigeyoshiIntegral means inequalities are obtained for the fractional derivatives of order p + lambda(0 <= p <= n, 0 <= lambda < 1) of functions belonging to a unified subclass of prestarlike functions. Relevant connections with various known integral means inequalities are also pointed out. Copyright (c) 2007.Öğe New applications of the Bernardi integral operator(MDPI AG, 2020) Owa, Shigeyoshi; Güney, Hatun ÖzlemLet A(p, n) be the class of f (z) which are analytic p-valent functions in the closed unit disk U = {z ∈ C: |z| ≤ 1}. The expression B-m-λf(z) is defined by using fractional integrals of order l for f (z) ∈ A(p, n). When m = 1 and l = 0, B-1 f (z) becomes Bernardi integral operator. Using the fractional integral B-m-λ f (z), the subclass Tp, n (αs, β, ρ; m, λ) of A(p, n) is introduced. In the present paper, we discuss some interesting properties for f (z) concerning with the class Tp, n (αs, β, ρ; m, λ). Also, some interesting examples for our results will be considered.Öğe New classes of certain analytic functions(Semnan Univ, 2022) Guney, H. Ozlem; Acu, Mugur; Owa, ShigeyoshiConsidering a function f(z) which is the extremal function for p-valently starlike of order a in the open unit disk, two new classes S-p*(m,alpha) and K-p(m, alpha) are introduced. The object of the present paper is to discuss some interesting problems of functions f (z) concerned with S-p* (m, alpha) and K-p (m, alpha).Öğe New extension of Alexander and Libera integral operators(Scientific Technical Research Council Turkey-TUBITAK, 2022) Güney, H. Özlem; Owa, ShigeyoshiLet T be the class of analytic functions in the open unit disc U with f (0) = 0 and f'(0) = 1. For f(z) is an element of T, the Alexander integral operator A(-1)f(z), the Libera integral operator L(-1)f(z) and the Bernardi integral operator B(-1)f(z) were considered before. Using A(-1)f(z) and L(-1)f(z), a new integral operator F(lambda)f (z) is considered. After discuss some properties of dominant for F(lambda)f(z), another new integral operator O(-1)f(z) of f(z) is an element of T is discussed. The object of the present paper is to discuss the dominant of new integral operators F(lambda)f(z) and O(-1)f(z) concerning with some starlike functions and convex functions in U.Öğe New integral operator for analytic functions(Hindawi Limited, 2024) Güney, Hatun Özlem; Owa, Shigeyoshi; Attiya, Adel A.Let Apn be the class of functions fz given by fz=zp+ap+nzp+n+ap+n+1zp+n+1+⋯ which are analytic in the open unit disk U. For fz∈Apn, new integral operators O-jfz and Ojfzj=0,1,2,⋯. are considered. The operators O-jfz and Ojfz satisfy OjO-jfz=O-jOjfz=fz and O-j∗Ojfz=Oj∗O-jfz=f∗fz for the convolution ∗ of O-jfz and Ojfz. In the present paper, the dominants for both operators O-jfz and Ojfz and subordinations for O-jfz and Ojfz are discussed. Also, new subclass Tpγm,δ,ρ;m,j concerning with m different boundary points is defined and discussed. Moreover, some interesting problems of Tpγm,δ,ρ;m,j associated with Ojfz are obtained. Furthermore, some interesting examples for our results are considered.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 New Properties of Analytic Functions(Mdpi, 2024) Guney, Hatun Ozlem; Owa, ShigeyoshiIn the present paper, we consider the class A of functions f(z) of the form f(z)=z+& sum;k=1 infinity a1+k3z1+k3 that are analytic in the open unit disc U. If a1+k3=0 for k not equal 3n (n=1,2,3,& ctdot;), then f(z) is given by f(z)=z+& sum;k=2 infinity akzk. For such functions f(z)is an element of A, some interesting properties for subordinations and strongly starlike functions are given. Also, some interesting examples for the results are shown.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 subordination result associated with certain subclass of analytic functions involving Salagean operator(Springer International Publishing Ag, 2007) Eker, Sevtap Sumer; Seker, Bilal; Owa, ShigeyoshiWe obtain an interesting subordination relation for Salagean-type certain analytic functions by using subordination theorem.Öğe Some general properties of analytic and p-valent functions(Univ Nis, Fac Sci Math, 2024) Eker, Sevtap Sumer; Guney, Hatun Ozlem; Owa, ShigeyoshiLet A(p) be the class of functions f (z) of the formf(z) = z(p) + a(p+1)z(p+1) + a(p+2)z(p+2) + . . . , (p is an element of N = {1, 2, 3, . . .})which are analytic in the open unit disc U. In this article, we consider some generalization properties of the functions in A(p) and generalize results by applying fractional derivatives.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 Subordination problems for certain meromorphic functions(Tusi Mathematical Research Group (TMRG), 2023) Güney, Hatun Özlem; Owa, ShigeyoshiLet ? be the class of meromorphic functions f of the form f(z) = 1/z + a0 + a1z + · · · that are analytic in the punctured disk U0. For f ? ?, operators Dnf with n ? Z = {…,?1, 0, 1,…} are introduced. Applying differential subordinations for analytic functions in the open unit disc U, some interesting properties of f ? ? with Dnf are discussed, and argument problems of Dnf are given. Also, we consider some simple problems for our results.Öğe A Subordination Result with Generalized Sakaguchi Univalent Functions Related to Complex Order(Belgian Mathematical Soc Triomphe, 2008) Guney, H. Ozlem; Owa, ShigeyoshiIn the present paper, we obtain an interesting subordination relation for a family of analytic functions of complex order by using subordination theorem.
