Subclasses of starlike functions associated with some hyperbola 1
|
|
- Darrell Simpson
- 5 years ago
- Views:
Transcription
1 General Mathematics Vol. 14, No , Subclasses of starlike functions associated with some hyperbola 1 Mugur Acu Abstract In this paper we define some subclasses of starlike functions associated with some hyperbola by using a generalized Sălăgean operator and we give some properties regarding these classes Mathematics Subject Classification: 30C45 Key words and phrases: Starlike functions, Libera-Pascu integral operator, Briot-Bouquet differential subordination, generalized Sălăgean operator 1 Introduction Let HU be the set of functions which are regular in the unit disc U, A = {f HU : f0 = f 0 1 = 0}, H u U = {f HU : f is univalent in U} and S = {f A : f is univalent in U}. 1 Received April 4, 2006 Accepted for publication in revised form April 10,
2 32 Mugur Acu Let D n be the Sălăgean differential operator see [12] defined as: D n : A A, n N and D 0 = D 1 = D = zf z, D n = DD n 1. Remark 1.1. If f S, = a j z j, z U then D n = j n a j z j. 1 We recall here the definition of the well - known class of starlike functions { S = f A : Re zf } z > 0, z U. Let consider the Libera-Pascu integral operator L a : A A defined as: = L a F z = 1 + a z a z 0 F t t a 1 dt, a C, Re a 0. Generalizations of the Libera-Pascu integral operator was studied by many mathematicians such are P.T. Mocanu in [7], E. Drăghici in [6] and D. Breaz in [5]. Definition 1.1.[4] Let n N and 0. We denote with D n defined by D n : A A, the operator D 0 =, D 1 = 1 + zf z = D, D n = D D n 1. Remark 1.2.[4] We observe that D n is a linear operator and for = a j z j we have D n = 1 + j 1 n a j z j.
3 Subclasses of starlike functions associated with some hyperbola 33 Also, it is easy to observe that if we consider = 1 in the above definition we obtain the Sălăgean differential operator. The next theorem is result of the so called admissible functions method introduced by P.T. Mocanu and S.S. Miller see [8], [9], [10]. Theorem 1.1. Let h convex in U and Re[βh γ] > 0, z U. If p HU with p0 = h0 and p satisfied the Briot-Bouquet differential subordination p zp z βp γ hz, then pz hz. In [1] is introduced the following operator: Definition 1.2. Let β, R, β 0, 0 and = denote by D β the linear operator defined by a j z j. We D β : A A, D β = 1 + j 1 β a j z j. Remark 1.3. It is easy to observe that for β = n N we obtain the Al- Oboudi operator D n and for β = n N, = 1 we obtain the Sălăgean operator D n. The purpose of this note is to define some subclasses of starlike functions associated with some hyperbola by using the operator D β defined above and to obtain some properties regarding these classes.
4 34 Mugur Acu 2 Preliminary results Definition 2.1. [13] A function f S is said to be in the class SHα if it satisfies zf z 2α 2 1 < Re for some α α > 0 and for all z U. { } 2 zf z + 2α 2 1, Remark 2.1. Geometric { interpretation: } zf z Let Ωα = : z U, f SHα. Then Ωα = {w = u + i v : v 2 < 4αu + u 2, u > 0}. Note that Ωα is the interior of a hyperbola in the right half-plane which is symmetric about the real axis and has vertex at the origin. Definition 2.2. [3] Let f S and α > 0. We say that the function f is in the class SH n α, n N, if D n+1 2α 2 1 < Re D n { } 2 D n+1 +2α 2 1, z U. D n Remark 2.2. Geometric interpretation: If we denote with p α the analytic and univalent functions with the properties p α 0 = 1, p α0 > 0 and p α U = Ωα see Remark 2.1, then f SH n α if and only if D n+1 p D n α z, where the symbol denotes the subordination in U. 1 + bz 1 + 4α 4α2 We have p α z = 1 + 2α 2α, b = bα = and the 1 z 1 + 2α 2 branch of the square root w is chosen so that Im w 0. Theorem 2.1. [3] If F z SH n α, α > 0, n N, and = L a F z, where L a is the integral operator defined by 1, then SH n α, α > 0, n N.
5 Subclasses of starlike functions associated with some hyperbola 35 Theorem 2.2. [3] Let n N and α > 0. If f SH n+1 α then f SH n α. 3 Main results 1 + bz Definition 3.1. Let β 0, 0, α > 0 and p α z = 1 + 2α 1 z 2α, 1 + 4α 4α2 where b = bα = and the branch of the square root w is chosen so that Im w 0. We say that a function S is in the 1 + 2α 2 class SH β, α if D β p α z, z U. Remark 3.1. Geometric interpretation: SH β, α if and only if D β take all values in the domain Ωα which is the interior of a hyperbola in the right half-plane which is symmetric about the real axis and has vertex at the origin see Remark 2.1 and Remark 2.2. Remark 3.2. It is easy to observe that for β = n N and = 1 we obtain in the above definition we obtain the class SH n α studied in [3] and for = 1, β = 0 we obtain the class SHα studied in [13]. Theorem 3.1. Let β 0, α > 0 and > 0. We have SH β+1, α SH β, α. Proof. Let SH β+1, α. With notation pz = Dβ+1, p0 = 1, D β
6 36 Mugur Acu 2 we obtain Also, we have β+2 = D D β D β = D β = 1 pz Dβ+2 D β 1 + j 1 β+2 a j z j 1 + j 1 β a j z j and or 3 We have z zp z = D β Dβ+1 z D β D β D β = z j 1 β+1 ja j z j 1 = pz z zp z = pz 1 + D β 1 + j 1 β ja j z j 1 D β j 1 + j 1 β+1 a j z j D β j 1 + j 1 β a j z j D β. j 1 + j 1 β+1 a j z j =
7 Subclasses of starlike functions associated with some hyperbola 37 = = = j j 1 β+1 a j z j = 1 + j 1 β+1 a j z j + = = = j j 1 β+1 a j z j = j j 1 β+1 a j z j = j j 1 β+1 a j z j = 1 + j j 1 β+1 a j z j = j 1 β+1 a j z j j 1 β+2 a j z j = = 1 = 1 z = 1 Dβ+1 + z + 1 Dβ+2 z = = 1 = 1 Similarly we have Dβ Dβ+2 1 j 1 + j 1 β a j z j = 1 From 3 we obtain = +. 1D β + Dβ+1. zp z = = D β pz 1Dβ + Dβ+1 D β =
8 38 Mugur Acu Thus or = 1 1p Dβ+2 D β From 2 we obtain where > 0. = 1 pz 1 + pz D β pz 2 zp z = Dβ+2 D β pz 2 D β = pz 2 + zp z. = 1 pz 2 + zp z = p zp z pz pz, From SH β+1, α we have p zp z pz p αz, with p0 = p α 0 = 1, α > 0, β 0, > 0, and Re p α z > 0 from here construction. In this conditions from Theorem 1.1, we obtain or This means SH β, α. pz p α z D β p α z. Theorem 3.2. Let β 0, α > 0 and 1. If F z SH β, α then = L a F z SH β, α, where L a is the Libera-Pascu integral operator defined by 1. =
9 Subclasses of starlike functions associated with some hyperbola 39 Proof. From 1 we have 1 + af z = a + zf z and, by using the linear operator, we obtain 1 + a F z = a + = a + ja j z j = 1 + j 1 β+1 ja j z j We have see the proof of the above theorem Thus or j 1 + j 1 β+1 a j z j = a F z = a + 1 = a = + 1 Dβ a F z = a Similarly, we obtain Then 1 + ad β F z = a Dβ + Dβ+1. F z D β F z = β+1 D D β + a Dβ+1 D β D β + a
10 40 Mugur Acu With notation we obtain 4 F z D β F z = D β = pz, p0 = 1, p a pz p a We have see the proof of the above theorem zp z = Dβ+2 β+1 D D β pz 2 = = Dβ+2 pz pz2. Thus = 1 pz pz 2 + zp z. Then, from 4, we obtain. F z D β F z = pz2 + zp a pz p a = zp z = p p a + 1 1, where a C, Re a 0, β 0, and 1. From F z SH β, α we have zp z p 1 p a p αz, where a C, Re a 0, α > 0, β 0, 1, and from her construction, we have Re p α z > 0. In this conditions we have from Theorem 1.1 we obtain pz p α z
11 Subclasses of starlike functions associated with some hyperbola 41 or D β p α z. This means = L a F z SH β, α. Remark 3.3. If we consider β = n N in the previously results we obtain the Theorem 3.1 and Theorem 3.2 from [2]. References [1] M. Acu and S. Owa, Note on a class of starlike functions, Proceedings of the International Short Point Research Work on Study on Calculus Operators in Univalent Function Theory - kyoto 2006 to appear. [2] M. Acu and S. Owa, On n-starlike functions associated with some hyperbola, IJMS to appear. [3] M. Acu, On a subclass of n-starlike functions associated with some hyperbola, General Mathematics, Vol. 13, No , [4] F.M. Al-Oboudi, On univalent funtions defined by a generalized Sălăgean operator, Ind. J. Math. Math. Sci. 2004, no , [5] D. Breaz, Operatori integrali pe spaţii de funcţii univalente, Editura Academiei Române, Bucureşti [6] E. Drăghici, Elemente de teoria funcţiilor cu aplicaţii la operatori integrali univalenţi, Editura Constant, Sibiu [7] P.T. Mocanu, Classes of univalent integral operators, J. Math. Anal. Appl. 157, 11991,
12 42 Mugur Acu [8] S. S. Miller and P. T. Mocanu, Differential subordonations and univalent functions, Mich. Math , [9] S. S. Miller and P. T. Mocanu, Univalent solution of Briot-Bouquet differential equations, J. Differential Equations , [10] S. S. Miller and P. T. Mocanu, On some classes of first-order differential subordinations, Mich. Math , [11] W. Rogosinski, On the coefficients of subordinate functions, Proc. London Math. Soc , [12] Gr. Sălăgean, Subclasses of univalent functions, Complex Analysis. Fifth Roumanian-Finnish Seminar, Lectures Notes in Mathematics, 1013, Springer-Verlag, 1983, [13] J. Stankiewicz and A. Wisniowska, Starlike functions associated with some hyperbola, Folia Scientiarum Universitatis Tehnicae Resoviensis 147, Matematyka , University Lucian Blaga of Sibiu Department of Mathematics Str. Dr. I. Raṭiu, No Sibiu, Romania acu mugur@yahoo.com
On a subclass of n-close to convex functions associated with some hyperbola
General Mathematics Vol. 13, No. 3 (2005), 23 30 On a subclass of n-close to convex functions associated with some hyperbola Mugur Acu Dedicated to Professor Dumitru Acu on his 60th anniversary Abstract
More informationOn Some α-convex Functions
Int. J. Open Problems Comput. Sci. Math., Vol. 1, No. 1, June 2008 On Some α-convex Functions Mugur Acu 1, Fatima Al-Oboudi 2, Maslina Darus 3, Shigeyoshi Owa 4 Yaşar Polato glu 5 and Emel Yavuz 5 1 Department
More informationCERTAIN DIFFERENTIAL SUPERORDINATIONS USING A GENERALIZED SĂLĂGEAN AND RUSCHEWEYH OPERATORS. Alb Lupaş Alina
Acta Universitatis Apulensis ISSN: 1582-5329 No. 25/211 pp. 31-4 CERTAIN DIFFERENTIAL SUPERORDINATIONS USING A GENERALIZED SĂLĂGEAN AND RUSCHEWEYH OPERATORS Alb Lupaş Alina Abstract. In the present paper
More informationCERTAIN DIFFERENTIAL SUBORDINATIONS USING A GENERALIZED SĂLĂGEAN OPERATOR AND RUSCHEWEYH OPERATOR. Alina Alb Lupaş
CERTAIN DIFFERENTIAL SUBORDINATIONS USING A GENERALIZED SĂLĂGEAN OPERATOR AND RUSCHEWEYH OPERATOR Alina Alb Lupaş Dedicated to Prof. H.M. Srivastava for the 70th anniversary Abstract In the present paper
More informationDIFFERENTIAL OPERATOR GENERALIZED BY FRACTIONAL DERIVATIVES
Miskolc Mathematical Notes HU e-issn 1787-2413 Vol. 12 (2011), No. 2, pp. 167 184 DIFFERENTIAL OPERATOR GENERALIZED BY FRACTIONAL DERIVATIVES RABHA W. IBRAHIM AND M. DARUS Received March 30, 2010 Abstract.
More informationA NOTE ON A SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY A GENERALIZED SĂLĂGEAN OPERATOR. Alina Alb Lupaş, Adriana Cătaş
Acta Universitatis Apulensis ISSN: 158-539 No. /010 pp. 35-39 A NOTE ON A SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY A GENERALIZED SĂLĂGEAN OPERATOR Alina Alb Lupaş, Adriana Cătaş Abstract. By means of
More informationThe Relationships Between p valent Functions and Univalent Functions
DOI:.55/auom-25-5 An. Şt. Univ. Ovidius Constanţa Vol. 23(),25, 65 72 The Relationships Between p valent Functions and Univalent Functions Murat ÇAĞLAR Abstract In this paper, we obtain some sufficient
More informationA note on a subclass of analytic functions defined by a generalized Sălăgean and Ruscheweyh operator
General Mathematics Vol. 17, No. 4 (2009), 75 81 A note on a subclass of analytic functions defined by a generalized Sălăgean and Ruscheweyh operator Alina Alb Lupaş, Adriana Cătaş Abstract By means of
More informationCoecient bounds for certain subclasses of analytic functions of complex order
Hacettepe Journal of Mathematics and Statistics Volume 45 (4) (2016), 1015 1022 Coecient bounds for certain subclasses of analytic functions of complex order Serap Bulut Abstract In this paper, we introduce
More informationBanach Journal of Mathematical Analysis ISSN: (electronic)
Banach J. Math. Anal. (008), no., 16 Banach Journal of Mathematical Analysis ISSN: 1735-8787 (electronic) http://www.math-analysis.org GENEALIZATION OF SǍLǍGEAN OPEATO FO CETAIN ANALYTIC FUNCTIONS ALAWIAH
More informationCoefficients estimates of some subclasses of analytic functions related with conic domain
DOI: 10.2478/auom-2013-0031 An. Şt. Univ. Ovidius Constanţa Vol. 212),2013, 181 188 Coefficients estimates of some subclasses of analytic functions related with conic domain Abstract In this paper, the
More informationOn α-uniformly close-to-convex and. quasi-convex functions with. negative coefficients
heoretical Mathematics & Applications, vol.3, no.2, 2013, 29-37 ISSN: 1792-9687 (print), 1792-9709 (online) Scienpress Ltd, 2013 On α-uniformly close-to-convex and quasi-convex functions with negative
More informationA best approximation property of the generalized spline functions
General Mathematics Vol. 16, No. 4 (2008), 25 33 A best approximation property of the generalized spline functions Adrian Branga Abstract In the introduction of this paper is presented the definition of
More informationSOME SUBCLASSES OF ANALYTIC FUNCTIONS DEFINED BY GENERALIZED DIFFERENTIAL OPERATOR. Maslina Darus and Imran Faisal
Acta Universitatis Apulensis ISSN: 1582-5329 No. 29/212 pp. 197-215 SOME SUBCLASSES OF ANALYTIC FUNCTIONS DEFINED BY GENERALIZED DIFFERENTIAL OPERATOR Maslina Darus and Imran Faisal Abstract. Let A denote
More informationA general coefficient inequality 1
General Mathematics Vol. 17, No. 3 (2009), 99 104 A general coefficient inequality 1 Sukhwinder Singh, Sushma Gupta and Sukhjit Singh Abstract In the present note, we obtain a general coefficient inequality
More informationConvolution properties for subclasses of meromorphic univalent functions of complex order. Teodor Bulboacă, Mohamed K. Aouf, Rabha M.
Faculty of Sciences Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Filomat 26:1 (2012), 153 163 DOI: 10.2298/FIL1201153B Convolution properties for subclasses of meromorphic
More informationA Structural Theorem of the Generalized Spline Functions 1
General Mathematics Vol. 17, No. 2 (2009), 135 143 A Structural Theorem of the Generalized Spline Functions 1 Adrian Branga Abstract In the introduction of this paper is presented the definition of the
More informationSome properties for α-starlike functions with respect to k-symmetric points of complex order
doi: 1.17951/a.217.71.1.1 A N N A L E S U N I V E R S I T A T I S M A R I A E C U R I E - S K Ł O D O W S K A L U B L I N P O L O N I A VOL. LXXI, NO. 1, 217 SECTIO A 1 9 H. E. DARWISH, A. Y. LASHIN and
More informationSOME APPLICATIONS OF SALAGEAN INTEGRAL OPERATOR. Let A denote the class of functions of the form: f(z) = z + a k z k (1.1)
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume LV, Number 1, March 2010 SOME APPLICATIONS OF SALAGEAN INTEGRAL OPERATOR Abstract. In this paper we introduce and study some new subclasses of starlike, convex,
More informationOn sandwich theorems for p-valent functions involving a new generalized differential operator
Stud. Univ. Babeş-Bolyai Math. 60(015), No. 3, 395 40 On sandwich theorems for p-valent functions involving a new generalized differential operator T. Al-Hawary, B.A. Frasin and M. Darus Abstract. A new
More informationOn Univalent Functions Defined by the Multiplier Differential Operator
Int. Journal of Math. Analysis, Vol. 6, 2012, no. 15, 735-742 On Univalent Functions Defined by the Multiplier Differential Operator Li Zhou College of Mathematics and Information Science JiangXi Normal
More informationSUBORDINATION RESULTS FOR CERTAIN SUBCLASSES OF UNIVALENT MEROMORPHIC FUNCTIONS
SUBORDINATION RESULTS FOR CERTAIN SUBCLASSES OF UNIVALENT MEROMORPHIC FUNCTIONS, P.G. Student, Department of Mathematics,Science College, Salahaddin University, Erbil, Region of Kurdistan, Abstract: In
More informationRosihan M. Ali, M. Hussain Khan, V. Ravichandran, and K. G. Subramanian. Let A(p, m) be the class of all p-valent analytic functions f(z) = z p +
Bull Korean Math Soc 43 2006, No 1, pp 179 188 A CLASS OF MULTIVALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS DEFINED BY CONVOLUTION Rosihan M Ali, M Hussain Khan, V Ravichandran, and K G Subramanian Abstract
More informationCertain classes of p-valent analytic functions with negative coefficients and (λ, p)-starlike with respect to certain points
BULETINUL ACADEMIEI DE ŞTIINŢE A REPUBLICII MOLDOVA. MATEMATICA Number 379), 2015, Pages 35 49 ISSN 1024 7696 Certain classes of p-valent analytic functions with negative coefficients and λ, p)-starlike
More informationAN EXTENSION OF THE REGION OF VARIABILITY OF A SUBCLASS OF UNIVALENT FUNCTIONS
AN EXTENSION OF THE REGION OF VARIABILITY OF A SUBCLASS OF UNIVALENT FUNCTIONS SUKHWINDER SINGH SUSHMA GUPTA AND SUKHJIT SINGH Department of Applied Sciences Department of Mathematics B.B.S.B. Engineering
More informationOn a subclass of analytic functions involving harmonic means
DOI: 10.1515/auom-2015-0018 An. Şt. Univ. Ovidius Constanţa Vol. 231),2015, 267 275 On a subclass of analytic functions involving harmonic means Andreea-Elena Tudor Dorina Răducanu Abstract In the present
More informationTwo Points-Distortion Theorems for Multivalued Starlike Functions
Int. Journal of Math. Analysis, Vol. 2, 2008, no. 17, 799-806 Two Points-Distortion Theorems for Multivalued Starlike Functions Yaşar Polato glu Department of Mathematics and Computer Science TC İstanbul
More informationDIFFERENTIAL SUBORDINATION RESULTS FOR NEW CLASSES OF THE FAMILY E(Φ, Ψ)
DIFFERENTIAL SUBORDINATION RESULTS FOR NEW CLASSES OF THE FAMILY E(Φ, Ψ) Received: 05 July, 2008 RABHA W. IBRAHIM AND MASLINA DARUS School of Mathematical Sciences Faculty of Science and Technology Universiti
More informationON CERTAIN CLASS OF UNIVALENT FUNCTIONS WITH CONIC DOMAINS INVOLVING SOKÓ L - NUNOKAWA CLASS
U.P.B. Sci. Bull., Series A, Vol. 80, Iss. 1, 018 ISSN 13-707 ON CERTAIN CLASS OF UNIVALENT FUNCTIONS WITH CONIC DOMAINS INVOLVING SOKÓ L - NUNOKAWA CLASS S. Sivasubramanian 1, M. Govindaraj, K. Piejko
More informationSubclasses of bi-univalent functions related to shell-like curves connected with Fibonacci numbers
Acta Univ. Sapientiae, Mathematica, 10, 1018 70-84 DOI: 10.478/ausm-018-0006 Subclasses of bi-univalent functions related to shell-like curves connected with Fibonacci numbers H. Özlem Güney Dicle University,
More informationConvex Functions and Functions with Bounded Turning
Tamsui Oxford Journal of Mathematical Sciences 26(2) (2010) 161-172 Aletheia University Convex Functions Functions with Bounded Turning Nikola Tuneski Faculty of Mechanical Engineering, Karpoš II bb, 1000
More informationSome applications of differential subordinations in the geometric function theory
Sokół Journal of Inequalities and Applications 2013, 2013:389 R E S E A R C H Open Access Some applications of differential subordinations in the geometric function theory Janus Sokół * Dedicated to Professor
More informationON THE FEKETE-SZEGÖ INEQUALITY FOR A CLASS OF ANALYTIC FUNCTIONS DEFINED BY USING GENERALIZED DIFFERENTIAL OPERATOR
Acta Universitatis Apulensis ISSN: 58-539 No. 6/0 pp. 67-78 ON THE FEKETE-SZEGÖ INEQUALITY FOR A CLASS OF ANALYTIC FUNCTIONS DEFINED BY USING GENERALIZED DIFFERENTIAL OPERATOR Salma Faraj Ramadan, Maslina
More informationOn differential subordinations in the complex plane
Nunokawa et al. Journal of Inequalities Applications 015) 015:7 DOI 10.1186/s13660-014-0536-9 R E S E A R C H Open Access On differential subordinations in the complex plane Mamoru Nunokawa 1, Nak Eun
More informationPROFESSOR PETRU T. MOCANU ON HIS 70 th BIRTHDAY
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume XLVI, Number 2, June 2001 PROFESSOR PETRU T. MOCANU ON HIS 70 th BIRTHDAY Professor Petru T. Mocanu was born on June 1, 2001 in Brăila, Romania. He attended
More informationSOME CRITERIA FOR STRONGLY STARLIKE MULTIVALENT FUNCTIONS
Bulletin of the Institute of Mathematics Academia Sinica (New Series) Vol. 7 (01), No. 3, pp. 43-436 SOME CRITERIA FOR STRONGLY STARLIKE MULTIVALENT FUNCTIONS DINGGONG YANG 1 AND NENG XU,b 1 Department
More informationHankel determinant for p-valently starlike and convex functions of order α
General Mathematics Vol. 17, No. 4 009, 9 44 Hankel determinant for p-valently starlike and convex functions of order α Toshio Hayami, Shigeyoshi Owa Abstract For p-valently starlike and convex functions
More informationSubordination and Superordination Results for Analytic Functions Associated With Convolution Structure
Int. J. Open Problems Complex Analysis, Vol. 2, No. 2, July 2010 ISSN 2074-2827; Copyright c ICSRS Publication, 2010 www.i-csrs.org Subordination and Superordination Results for Analytic Functions Associated
More informationNew Results in the Theory of Differential Subordinations and Superordinations
Babeş-Bolyai University of Cluj-Napoca Faculty of Mathematics and Computer Science Habilitation Thesis in Mathematics presented by Teodor Bulboacă New Results in the Theory of Differential Subordinations
More informationThe Noor Integral and Strongly Starlike Functions
Journal of Mathematical Analysis and Applications 61, 441 447 (001) doi:10.1006/jmaa.001.7489, available online at http://www.idealibrary.com on The Noor Integral and Strongly Starlike Functions Jinlin
More informationINTEGRAL MEANS OF UNIVALENT SOLUTION FOR FRACTIONAL EQUATION IN COMPLEX PLANE. Rabha W. Ibrahim and Maslina Darus
Acta Universitatis Apulensis ISSN: 1582-5329 No. 23/21 pp. 39-47 INTEGRAL MEANS OF UNIVALENT SOLUTION FOR FRACTIONAL EQUATION IN COMPLEX PLANE Rabha W. Ibrahim and Maslina Darus Abstract. Integral means
More informationSTRONG DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF NEW GENERALIZED DERIVATIVE OPERATOR. Anessa Oshah and Maslina Darus
Korean J. Math. 23 2015, No. 4, pp. 503 519 http://dx.doi.org/10.11568/jm.2015.23.4.503 STRONG DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF NEW GENERALIZED DERIVATIVE OPERATOR Anessa Oshah and Maslina
More informationON STRONG ALPHA-LOGARITHMICALLY CONVEX FUNCTIONS. 1. Introduction and Preliminaries
ON STRONG ALPHA-LOGARITHMICALLY CONVEX FUNCTIONS NIKOLA TUNESKI AND MASLINA DARUS Abstract. We give sharp sufficient conditions that embed the class of strong alpha-logarithmically convex functions into
More informationDIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF ANALYTIC FUNCTIONS DEFINED BY THE MULTIPLIER TRANSFORMATION
M athematical I nequalities & A pplications Volume 12, Number 1 2009), 123 139 DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF ANALYTIC FUNCTIONS DEFINED BY THE MULTIPLIER TRANSFORMATION ROSIHAN M. ALI,
More informationA Note on Coefficient Inequalities for (j, i)-symmetrical Functions with Conic Regions
BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN (p) 2303-4874 ISSN (o) 2303-4955 wwwimviblorg /JOURNALS / BULLETIN Vol 6(2016) 77-87 Former BULLETIN OF THE SOCIETY OF MATHEMATICIANS BANJA
More informationAbstract. For the Briot-Bouquet differential equations of the form given in [1] zu (z) u(z) = h(z),
J. Korean Math. Soc. 43 (2006), No. 2, pp. 311 322 STRONG DIFFERENTIAL SUBORDINATION AND APPLICATIONS TO UNIVALENCY CONDITIONS José A. Antonino Astract. For the Briot-Bouquet differential equations of
More informationRosihan M. Ali and V. Ravichandran 1. INTRODUCTION
TAIWANESE JOURNAL OF MATHEMATICS Vol. 14, No. 4, pp. 1479-1490, August 2010 This paper is available online at http://www.tjm.nsysu.edu.tw/ CLASSES OF MEROMORPHIC α-convex FUNCTIONS Rosihan M. Ali and V.
More informationj(z) > + FZ f(z) z + oz f(z) 1-.F < 1-.F zf (z) } 1 E (z 6 U,F 1). (1.3) >/(z e u) ANGULAR ESTIMATIONS OF CERTAIN INTEGRAL OPERATORS
Internat. J. Math. & Math. Sci. VOL. 1 NO. (1998) 369374 369 ANGULAR ESTIMATIONS OF CERTAIN INTEGRAL OPERATORS NAK EUN CHO, IN HWA KIM JI A KIM Department of Applied Mathematics Pukyong National University
More informationSOME RESULTS OF p VALENT FUNCTIONS DEFINED BY INTEGRAL OPERATORS. Gulsah Saltik Ayhanoz and Ekrem Kadioglu
Acta Universitatis Aulensis ISSN: 1582-5329 No. 32/2012. 69-85 SOME ESULTS OF VALENT FUNCTIONS EFINE BY INTEAL OPEATOS ulsah Saltik Ayhanoz and Ekre Kadioglu Abstract. In this aer, we derive soe roerties
More informationResearch Article Differential Subordinations of Arithmetic and Geometric Means of Some Functionals Related to a Sector
International Journal of Mathematics and Mathematical Sciences Volume 2011, Article ID 205845, 19 pages doi:10.1155/2011/205845 Research Article Differential Subordinations of Arithmetic and Geometric
More informationDifferential subordination related to conic sections
J. Math. Anal. Appl. 317 006 650 658 www.elsevier.com/locate/jmaa Differential subordination related to conic sections Stanisława Kanas Department of Mathematics, Rzeszów University of Technology, W. Pola,
More informationORDER. 1. INTRODUCTION Let A denote the class of functions of the form
SARAJEVO JOURNAL OF MATHEMATICS Vol.10 (22) (2014), 55 60 DOI: 10.5644/SJM.10.1.07 ON UNIFIED CLASS OF γ-spirallike FUNCTIONS OF COMPLEX ORDER T. M. SEOUDY ABSTRACT. In this paper, we obtain a necessary
More informationdenote the subclass of the functions f H of the form H of the form
Scholars Journal of Engineering and Technology (SJET) Sch. J. Eng. Tech., 05; 3(4C):55-59 Scholars Academic and Scientific Publisher (An International Publisher for Academic and Scientific Resources) www.saspublisher.com
More informationHADAMARD PRODUCT OF CERTAIN CLASSES OF FUNCTIONS
Journal of Applied Analysis Vol. 11, No. 1 (2005), pp. 145 151 HADAMARD PRODUCT OF CERTAIN CLASSES OF FUNCTIONS K. PIEJKO Received June 16, 2004 and, in revised form, November 22, 2004 Abstract. In this
More informationA subclass of analytic functions
Stud. Univ. Babeş-Bolyai Math. 57(2012), No. 2, 277 282 A subclass of analytic functions Andreea-Elena Tudor Abstract. In the present paper, by means of Carlson-Shaffer operator and a multiplier transformation,
More informationOn second-order differential subordinations for a class of analytic functions defined by convolution
Available online at www.isr-publications.co/jnsa J. Nonlinear Sci. Appl., 1 217), 954 963 Research Article Journal Hoepage: www.tjnsa.co - www.isr-publications.co/jnsa On second-order differential subordinations
More informationOn certain subclasses of analytic functions
Stud. Univ. Babeş-Bolyai Math. 58(013), No. 1, 9 14 On certain subclasses of analytic functions Imran Faisal, Zahid Shareef and Maslina Darus Abstract. In the present paper, we introduce and study certain
More informationDIFFERENTIAL SUBORDINATION FOR MEROMORPHIC MULTIVALENT QUASI-CONVEX FUNCTIONS. Maslina Darus and Imran Faisal. 1. Introduction and preliminaries
FACTA UNIVERSITATIS (NIŠ) SER. MATH. INFORM. 26 (2011), 1 7 DIFFERENTIAL SUBORDINATION FOR MEROMORPHIC MULTIVALENT QUASI-CONVEX FUNCTIONS Maslina Darus and Imran Faisal Abstract. An attempt has been made
More informationSecond Hankel Determinant Problem for a Certain Subclass of Univalent Functions
International Journal of Mathematical Analysis Vol. 9, 05, no. 0, 493-498 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/ijma.05.55 Second Hankel Determinant Problem for a Certain Subclass of Univalent
More informationAPPLYING RUSCHEWEYH DERIVATIVE ON TWO SUB-CLASSES OF BI-UNIVALENT FUNCTIONS
International Journal of Basic & Applied Sciences IJBAS-IJENS Vol:1 No:06 68 APPLYING RUSCHEWEYH DERIVATIVE ON TWO SUB-CLASSES OF BI-UNIVALENT FUNCTIONS ABDUL RAHMAN S. JUMA 1, FATEH S. AZIZ DEPARTMENT
More informationProperties of Starlike Functions with Respect to Conjugate Points
Int. J. Contemp. Math. Sciences, Vol. 5, 1, no. 38, 1855-1859 Properties of Starlike Functions with Respect to Conjugate Points Suci Aida Fitri Mad Dahhar and Aini Janteng School of Science and Technology,
More informationCOEFFICIENT BOUNDS FOR A SUBCLASS OF BI-UNIVALENT FUNCTIONS
TWMS J. Pure Appl. Math., V.6, N.2, 205, pp.80-85 COEFFICIENT BOUNDS FOR A SUBCLASS OF BI-UNIVALENT FUNCTIONS ŞAHSENE ALTINKAYA, SIBEL YALÇIN Abstract. An analytic function f defined on the open unit disk
More informationOn a New Subclass of Salagean Type Analytic Functions
Int. Journal of Math. Analysis, Vol. 3, 2009, no. 14, 689-700 On a New Subclass of Salagean Type Analytic Functions K. K. Dixit a, V. Kumar b, A. L. Pathak c and P. Dixit b a Department of Mathematics,
More informationOn Analytic Properties of a Sigmoid Function
International Journal of Mathematics and Computer Science, 13(2018), no. 2, 171 178 M CS On Analytic Properties of a Sigmoid Function Uzoamaka A. Ezeafulukwe 1, Maslina Darus 2, Olubunmi Abidemi Fadipe-Joseph
More informationQuasi-Convex Functions with Respect to Symmetric Conjugate Points
International Journal of Algebra, Vol. 6, 2012, no. 3, 117-122 Quasi-Convex Functions with Respect to Symmetric Conjugate Points 1 Chew Lai Wah, 2 Aini Janteng and 3 Suzeini Abdul Halim 1,2 School of Science
More informationThe Order of Starlikeness of New p-valent Meromorphic Functions
Int. Journal of Math. Analysis, Vol. 6, 2012, no. 27, 1329-1340 The Order of Starlikeness of New p-valent Meromorphic Functions Aabed Mohammed and Maslina Darus School of Mathematical Sciences Faculty
More informationON SOME LENGTH PROBLEMS FOR ANALYTIC FUNCTIONS
Nunokawa, M. and Sokół, J. Osaka J. Math. 5 (4), 695 77 ON SOME LENGTH PROBLEMS FOR ANALYTIC FUNCTIONS MAMORU NUNOKAWA and JANUSZ SOKÓŁ (Received December 6, ) Let A be the class of functions Abstract
More informationQuasiHadamardProductofCertainStarlikeandConvexFunctions
Global Journal of Science Frontier Research: F Mathematics and Decision Sciences Volume 15 Issue 10 Version 1.0 Year 2015 Type : Double Blind Peer Reviewed International Research Journal Publisher: Global
More informationDIFFERENTIAL SANDWICH THEOREMS FOR SOME SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING A LINEAR OPERATOR. 1. Introduction
DIFFERENTIAL SANDWICH THEOREMS FOR SOME SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING A LINEAR OPERATOR T. N. SHAMMUGAM, C. RAMACHANDRAN, M. DARUS S. SIVASUBRAMANIAN Abstract. By making use of the familiar
More informationResearch Article A Study on Becker s Univalence Criteria
Abstract and Applied Analysis Volume 20, Article ID 75975, 3 pages doi:0.55/20/75975 Research Article A Study on Becker s Univalence Criteria Maslina Darus and Imran Faisal School of Mathematical Sciences,
More informationSTARLIKE MAPPINGS OF ORDER α ON THE UNIT BALL IN COMPLEX BANACH SPACES
GLASNIK MATEMATIČKI Vol. 36(56)(2001), 39 48 STARLIKE MAPPINGS OF ORDER α ON THE UNIT BALL IN COMPLEX BANACH SPACES Hidetaka Hamada, Gabriela Kohr and Piotr Liczberski Kyushu Kyoritsu University, Japan
More informationDIFFERENTIAL SANDWICH THEOREMS FOR SOME SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING A LINEAR OPERATOR. 1. Introduction
Acta Math. Univ. Comenianae Vol. LXXVI, 2(2007), pp. 287 294 287 DIFFERENTIAL SANDWICH THEOREMS FOR SOME SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING A LINEAR OPERATOR T. N. SHAMMUGAM, C. RAMACHANDRAN, M.
More informationA NOTE ON UNIVALENT FUNCTIONS WITH FINITELY MANY COEFFICIENTS. Abstract
A NOTE ON UNIVALENT FUNCTIONS WITH FINITELY MANY COEFFICIENTS M. Darus, R.W. Ibrahim Abstract The main object of this article is to introduce sufficient conditions of univalency for a class of analytic
More informationDifferential Subordination and Superordination for Multivalent Functions Involving a Generalized Differential Operator
Differential Subordination Superordination for Multivalent Functions Involving a Generalized Differential Operator Waggas Galib Atshan, Najah Ali Jiben Al-Ziadi Departent of Matheatics, College of Coputer
More informationCERTAIN SUBCLASSES OF STARLIKE AND CONVEX FUNCTIONS OF COMPLEX ORDER
Hacettepe Journal of Mathematics and Statistics Volume 34 (005), 9 15 CERTAIN SUBCLASSES OF STARLIKE AND CONVEX FUNCTIONS OF COMPLEX ORDER V Ravichandran, Yasar Polatoglu, Metin Bolcal, and Aru Sen Received
More informationDifferential subordination theorems for new classes of meromorphic multivalent Quasi-Convex functions and some applications
Int. J. Adv. Appl. Math. and Mech. 2(3) (2015) 126-133 (ISSN: 2347-2529) Journal homepage: www.ijaamm.com International Journal of Advances in Applied Mathematics and Mechanics Differential subordination
More informationCertain properties of a new subclass of close-to-convex functions
Arab J Math (212) 1:39 317 DOI 1.17/s465-12-29-y RESEARCH ARTICLE Pranay Goswami Serap Bulut Teodor Bulboacă Certain properties of a new subclass of close-to-convex functions Received: 18 November 211
More informationSubordinate Solutions of a Differential Equation
Subordinate Solutions of a Differential Equation Stacey Muir Abstract In 2003, Ruscheweyh and Suffridge settled a conjecture of Pólya and Schoenberg on subordination of the de la Vallée Poussin means of
More informationUniformly convex functions II
ANNALES POLONICI MATHEMATICI LVIII. (199 Uniformly convex functions II by Wancang Ma and David Minda (Cincinnati, Ohio Abstract. Recently, A. W. Goodman introduced the class UCV of normalized uniformly
More informationOn a subclass of certain p-valent starlike functions with negative coefficients 1
General Mathematics Vol. 18, No. 2 (2010), 95 119 On a subclass of certain p-valent starlike functions with negative coefficients 1 S. M. Khairnar, N. H. More Abstract We introduce the subclass T Ω (n,
More informationInclusion and argument properties for certain subclasses of multivalent functions defined by the Dziok-Srivastava operator
Advances in Theoretical Alied Mathematics. ISSN 0973-4554 Volume 11, Number 4 016,. 361 37 Research India Publications htt://www.riublication.com/atam.htm Inclusion argument roerties for certain subclasses
More informationOn Multivalent Functions Associated with Fixed Second Coefficient and the Principle of Subordination
International Journal of Mathematical Analysis Vol. 9, 015, no. 18, 883-895 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ijma.015.538 On Multivalent Functions Associated with Fixed Second Coefficient
More informationInt. J. Open Problems Complex Analysis, Vol. 3, No. 1, March 2011 ISSN ; Copyright c ICSRS Publication,
Int. J. Open Problems Complex Analysis, Vol. 3, No. 1, March 211 ISSN 274-2827; Copyright c ICSRS Publication, 211 www.i-csrs.org Coefficient Estimates for Certain Class of Analytic Functions N. M. Mustafa
More informationCoefficient Estimate for Two Subclasses with Certain Close-to-Convex Functions
Int. Journal of Math. Analysis, Vol. 5, 2011, no. 8, 381-386 Coefficient Estimate for Two Subclasses with Certain Close-to-Convex Functions Liangpeng Xiong The College of Engineering and Technical of Chengdou
More informationDifferential Operator of a Class of Meromorphic Univalent Functions With Negative Coefficients
Differential Operator of a Class of Meromorphic Univalent Functions With Negative Coefficients Waggas Galib Atshan and Ali Hamza Abada Department of Mathematics College of Computer Science and Mathematics
More informationSubclass Of K Uniformly Starlike Functions Associated With Wright Generalized Hypergeometric Functions
P a g e 52 Vol.10 Issue 5(Ver 1.0)September 2010 Subclass Of K Uniformly Starlike Functions Associated With Wright Generalized Hypergeometric Functions G.Murugusundaramoorthy 1, T.Rosy 2 And K.Muthunagai
More informationA NEW CLASS OF MEROMORPHIC FUNCTIONS RELATED TO CHO-KWON-SRIVASTAVA OPERATOR. F. Ghanim and M. Darus. 1. Introduction
MATEMATIQKI VESNIK 66, 1 14, 9 18 March 14 originalni nauqni rad research paper A NEW CLASS OF MEROMORPHIC FUNCTIONS RELATED TO CHO-KWON-SRIVASTAVA OPERATOR F. Ghanim and M. Darus Abstract. In the present
More informationSome Further Properties for Analytic Functions. with Varying Argument Defined by. Hadamard Products
International Mathematical Forum, Vol. 10, 2015, no. 2, 75-93 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2015.412205 Some Further Properties for Analytic Functions with Varying Argument
More informationOn certain subclasses of analytic functions associated with generalized struve functions
BULETINUL ACADEMIEI DE ŞTIINŢE A REPUBLICII MOLDOVA. MATEMATICA Number 3(79), 2015, Pages 3 13 ISSN 1024 7696 On certain subclasses of analytic functions associated with generalized struve functions G.
More informationInitial Coefficient Bounds for a General Class of Bi-Univalent Functions
Filomat 29:6 (2015), 1259 1267 DOI 10.2298/FIL1506259O Published by Faculty of Sciences Mathematics, University of Niš, Serbia Available at: http://.pmf.ni.ac.rs/filomat Initial Coefficient Bounds for
More informationSANDWICH-TYPE THEOREMS FOR A CLASS OF INTEGRAL OPERATORS ASSOCIATED WITH MEROMORPHIC FUNCTIONS
East Asian Mathematical Journal Vol. 28 (2012), No. 3, pp. 321 332 SANDWICH-TYPE THEOREMS FOR A CLASS OF INTEGRAL OPERATORS ASSOCIATED WITH MEROMORPHIC FUNCTIONS Nak Eun Cho Abstract. The purpose of the
More informationSOME INCLUSION PROPERTIES OF STARLIKE AND CONVEX FUNCTIONS ASSOCIATED WITH HOHLOV OPERATOR. II
italian journal of pure and applied mathematics n. 37 2017 117 126 117 SOME INCLUSION PROPERTIES OF STARLIKE AND CONVEX FUNCTIONS ASSOCIATED WITH HOHLOV OPERATOR. II M. Kasthuri K. Vijaya 1 K. Uma School
More informationFekete-Szegö Problem for Certain Subclass of Analytic Univalent Function using Quasi-Subordination
Mathematica Aeterna, Vol. 3, 203, no. 3, 93-99 Fekete-Szegö Problem for Certain Subclass of Analytic Univalent Function using Quasi-Subordination B. Srutha Keerthi Department of Applied Mathematics Sri
More informationDIFFERENTIAL SUBORDINATION ASSOCIATED WITH NEW GENERALIZED DERIVATIVE OPERATOR
ROMAI J., v.12, no.1(2016), 77 89 DIFFERENTIAL SUBORDINATION ASSOCIATED WITH NEW GENERALIZED DERIVATIVE OPERATOR Anessa Oshah, Maslina Darus School of Mathematical Sciences, Faculty of Science and Technology,
More informationSteepest descent approximations in Banach space 1
General Mathematics Vol. 16, No. 3 (2008), 133 143 Steepest descent approximations in Banach space 1 Arif Rafiq, Ana Maria Acu, Mugur Acu Abstract Let E be a real Banach space and let A : E E be a Lipschitzian
More informationCOEFFICIENTS OF BI-UNIVALENT FUNCTIONS INVOLVING PSEUDO-STARLIKENESS ASSOCIATED WITH CHEBYSHEV POLYNOMIALS
Khayyam J. Math. 5 (2019), no. 1, 140 149 DOI: 10.2204/kjm.2019.8121 COEFFICIENTS OF BI-UNIVALENT FUNCTIONS INVOLVING PSEUDO-STARLIKENESS ASSOCIATED WITH CHEBYSHEV POLYNOMIALS IBRAHIM T. AWOLERE 1, ABIODUN
More informationGEOMETRICAL AND ANALYTICAL PROPERTIES OF SOME CLASSES OF UNIVALENT FUNCTIONS
BABEŞ-BOLYAI UNIVERSITY, CLUJ-NAPOCA FACULTY OF MATHEMATICS AND COMPUTER SCIENCE GABRIELA ROXANA ŞENDRUŢIU GEOMETRICAL AND ANALYTICAL PROPERTIES OF SOME CLASSES OF UNIVALENT FUNCTIONS Ph.D. Thesis Summary
More informationResults regarding the argument of certain p-valent analytic functions defined by a generalized integral operator
El-Ashwah ournal of Inequalities and Applications 1, 1:35 http://www.journalofinequalitiesandapplications.co/content/1/1/35 RESEARCH Results regarding the arguent of certain p-valent analytic functions
More informationarxiv: v1 [math.cv] 19 Jul 2012
arxiv:1207.4529v1 [math.cv] 19 Jul 2012 On the Radius Constants for Classes of Analytic Functions 1 ROSIHAN M. ALI, 2 NAVEEN KUMAR JAIN AND 3 V. RAVICHANDRAN 1,3 School of Mathematical Sciences, Universiti
More informationSome Geometric Properties of a Certain Subclass of Univalent Functions Defined by Differential Subordination Property
Gen. Math. Notes Vol. 20 No. 2 February 2014 pp. 79-94 SSN 2219-7184; Copyright CSRS Publication 2014 www.i-csrs.org Available free online at http://www.geman.in Some Geometric Properties of a Certain
More information