denote the subclass of the functions f H of the form H of the form
|
|
- Rosamond Brooks
- 5 years ago
- Views:
Transcription
1 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) ISSN 3-435X (Online) ISSN (Print) Research Article On sandwich theorems for certain analytic functions Jing Wang, Lifeng Guo School of Mathematica Science and Technology, Northeast Petroleum University, Daqing 6338, China. *Corresponding author Jing Wang Abstract: In this paper, we derive some subordination and superordination results for certain normalied analytic functions in the open unit disk. Keywords: univalent functions; starlike functions; subordination; superordination INTRODUCTION Let H denote the class of analytic functions in the open unit disc U { C }, and H[ a n] denote the subclass of the functions f H of the form Also,Let A be the subclass the functions f f () a a a n n n n () H of the form f () a a () 3 3 A function f A is said to be in the class S of starlike functions in U, if it satisfies the inequality Re( ) 0 U Furthermore, a function f A is said to be in the class C of convex functions in U, if it f ( ) f ( ) satisfies the inequality Re( ) 0 U f ( ) f( ) Let and F () be analytic in U, we say that the function is subordinate to F () in U, if there exists an analytic function w () in U such that w(), and f ( ) F( w( )), denoted by f p F or f ( ) p F( ). If F () is univalent in U, the subordination is equivalent to f(0) F(0) and f ( U) F( U). 3 Let ph H and let ( rst ) C U C. If p and ( p( ) p( ) p ( ) ) are univalent and if p satisfies the second-order superordination h ( ) ( p( ) p ( ) p ( ) ) p (3) p is a solution of the differential superordination (3). (If f is subordinate to F, F is superordinate to f.) An analytic function q is called a subordinant if qp p for all p satisfying (3). A univalent subordinant Q that satisfies qp Q for all subordinants q of (3) is said to be the best subordinant. Recently Miller and Mocanu [] obtained conditions on hq and for which the following implication holds: h( ) p ( p( ) p( ) p ( ) ) q( ) p p( ) (4) Using the results of Miller and Mocanu [], Bulboacǎ [] considered certain classes of first-order differential superordinations as well as superordination-preserving integral operators [3]. Ali et al. [4] have used the results of Bulboacǎ [] and obtained sufficient conditions for certain normalied analytic functions to satisfy 55
2 Jing Wang et al., Sch. J. Eng. Tech., 05; 3(4C):55-59 f () q( ) p p q( ) (5) where q and q are given univalent functions in U with q (0) and q (0). Shanmugam et al. [5] obtained sufficient conditions for normalied analytic functions to satisfy f ( ) f ( ) q ( ) p p q( ) andq ( ) p p q ( ) (6) f ( ) f ( ) where q and q are given univalent functions in U with q (0) and q (0), while Obradović and Owa [6] obtained subordination results with the quantity ( f ( ) ) (see also [7]). For 0, a function f ( ) N( ) if and only if f () A and f () Re{ ( ) } 0 U (7) f ( ) f ( ) N( ) was introduced by M.Obradović [8] recently, and he called this class of functions to be non-bailevič type. Tuneski and Darus [9] obtained Fekete-Segö inequality for the non-baileviˇc class of functions. Using this non- Bailevič class, Wang et al. [0] studied many subordination results for the class N( A B) defined as f ( ) A N( A B) { f ( ) A ( )( ) ( ) p U} (8) f ( ) f ( ) f ( ) B where 0 C B A B A R. The main object of the present sequel to the aforementioned works is to apply a method based on the differential subordination in order to derive several subordination results. Furthermore, we obtain the previous results of Srivastava and Lashin [7], Singh [], Shanmugam et al. [] and Obradović andowa [6] as special cases of some of the results presented here. Some lemmas To prove our main result, we will need the following definition and lemmas: DEFINITION [] Denote by the set of all functions that are analytic and injective on U E( f ), where E( f ) { U lim f ( ) } (9) and are such that f ( ) 0 for U E( f ). U and [5] Let q be univalent in U and let C with p( ) p q( ) and q is the best dominant. Re( ) max{0 } If p () is analytic in q( ) q( ) Re p( ) p( ) p q( ) q( ) (0) [] Let q be convex univalent in U and let C with Re( ) 0 If p( ) H[ q(0) ] p( ) p( ) is univalent in U, and q( ) q( ) p p( ) p( ) () q( ) p p( ) and q is the best subordinant. and 56
3 Jing Wang et al., Sch. J. Eng. Tech., 05; 3(4C):55-59 [3] Let q be univalent in U and let be analytic in a domain containing qu ( ) with ( w) 0 when w q( U). Set h( ) q( ) ( q( )), F( ) ( q( )) h( ) Suppose that () h () is starlike univalent in U ; () If Re( ) 0 for U F( ) h ( ) p( ) q( ) ( p( )) p( ) ( F( )) ( q( )) q( ) ( q( )) p and q() is the best dominant. p () [3] Let q be convex univalent in U, and let be analytic in a domain containing ( ) () q ( ) ( q( )) is starlike univalent in U ; ( q( ) () Re( ( q( )) ) 0 for U. If p( ) H[ q(0) ], with pu ( ) and ( p( )) p( ) ( p( )) is univalent in U and ( q( )) q( ) ( q( )) ( p( )) p( ) ( p( )) q( ) p p( ) and q is the best subordinant. Sandwich theroems By using., we first prove the following Theorem. qu. Suppose that p (3) Theorem 3..Let q () be univalent in U, 0 and C. Further assume that q() Re{ } max{0 Re } q() If f ( ) A g( ) S, g( ) g( ) f ( ) g( ) ( ) ( )( ) q( ) q( ) f ( ) g( ) f ( ) f ( ) implies that and q () is the best dominant. (4) p (5) g () ( ) p q ( ) (6) Proof. Define the function p () by g () p ( ) ( ) (7) Then a computation shows that g( ) g( ) f ( ) g( ) ( ) ( )( ) p( ) p( ) (8) f ( ) g( ) f ( ) f ( ) Then we obtain that p( ) p( ) p q( ) q( ) (9) By using.,we have the result. 57
4 Jing Wang et al., Sch. J. Eng. Tech., 05; 3(4C):55-59 Theorem 3..Let q () be convex univalent in U, 0, C ( ) Hq [ (0) ] and g( ) f ( ) be univalent in U. If and q () is the best subordinant. Proof. Let g( ) f ( ) with Re( ) 0. Suppose g( ) g( ) f ( ) g( ) ( ) ( )( ) (0) f ( ) g( ) f ( ) f ( ) g( ) g( ) f ( ) g( ) q( ) q( ) p ( ) ( )( ) () f ( ) g( ) f ( ) f ( ) g () q ( ) p ( ) () p ( ) ( ). Then Theorem 3. follows by an application of.. Combining the results of differential subordination and superordination, we obtain the following sandwich result. Corollary 3.3.Let () q be univalent and let q () be convex univalent in U, 0 and C with Re( ) 0. Suppose q () satisfies (4). If g( ) ( ) Hq [ (0) ], f ( ) ( ) ( )( ) is g ( ) g ( ) f ( ) g ( ) f ( ) g( ) f ( ) f ( ) univalent in U, and g( ) g( ) f ( ) g( ) q ( ) q ( ) p ( ) ( )( ) p q( ) q( ) (3) f ( ) g( ) f ( ) f ( ) g () q( ) p ( ) p q( ) (4) and q () and q () are respectively the best subordinant and the best dominant. For and g(), we get the following corollary. Corollary 3.4.Let () q be univalent and let q () be convex univalent in U, 0. Suppose q () g( ) (4). If ( ) f ( ) Hq [ (0) ], ( )( ) is univalent in U, and and () f ( ) q and q () f ( ) f ( ) satisfies f ( ) q ( ) q ( ) p ( )( ) p q( ) q( ) (5) f ( ) f ( ) q( ) p ( ) p q( ) (6) are respectively the best subordinant and best dominant. 4. Open Problem Let H be the class of analytic functions in U { C }, and H[ a p] be the subclass of H consisting of functions of the form p p f () a a a (7) p p Let Ap ( ) be the subclass of H consisting of functions of the form f () a a (8) p p p p p 58
5 Jing Wang et al., Sch. J. Eng. Tech., 05; 3(4C):55-59 A function f A( p) is said to be in the class S ( p) of p -valent starlike functions in U, if it satisfies the inequality Re( ) 0 U f ( ) pf ( ) Let f ( ) A( p) and g( ) S ( p) following implication holds:. We can consider sufficient conditions on hq q and for which the g () q( ) p ( ) p q( ) (9) or ( ) f ( ) f ( ) q( ) p ( ) p q( ) (30) g () where 0 and 0. REFERENCES. Miller SS, Mocanu PT; Subordinants of differential superordinations. Complex variables, 003; 48(0): Bulboacǎ T; Classes of first-order differential superordinations, Demonstratio Mathematica, 00; 35(): Bulboacǎ T; A class of superordination-preserving integral operators, IndagationesMathematicae. New Series, 00; 3(3): M Ali R, Ravichandran V, Hussain Khan M, Subramanian KG; Differential Sandwich Theorems For Certain Analytic Functions. Far East Journal of Mathematical Sciences, 004; 5(): Shanmugam TN, Ravichandran V, Sivasubramanian S; Differential sandwich theorems for some subclasses of analytic functions, The Australian Journal of Mathematical Analysis and Applications, 006; 3(). 6. Obradović M, Owa S; On certain properties for some classes of starlike functions, Journal of Mathematical Analysis and Applications, 990; 45(): Srivastava HM, Lashin AY; Some applications of the Briot-Bouquet differential subordination. J. Inequal. Pure Appl. Math, 005; 6(): Obradovic M, A class of univalent functions.hokkaido Math, 998; 7: Tuneski N, Darus M; Fekete-Segö functional for non-bailevič functions, ActaMathematica. Academiae Paedagogicae Nyíregyháiensis. New Series, 00; 8(): Wang Z, Gao C, Liao M; On certain generalied class of non-bailevič functions, ActaMathematica. Academiae Paedagogicae Nyíregyháiensis. New Series, 005; (): Singh V; On some criteria for univalence and starlikeness, Indian Journal of Pure and Applied Mathematics, 003; 34(4): Shanmugam TN, Sivasubramanian S, Silverman H; On sandwich theorems for some classes of analytic functions, International Journal of Mathematics and Mathematical Sciences, Miller SS, Mocanu PT; Differential Subordinations. Theory and Applications, Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, 000; 5. 59
Subordination 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 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 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 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 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 informationResearch Article Subordination and Superordination on Schwarzian Derivatives
Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 008, Article ID 7138, 18 pages doi:10.1155/008/7138 Research Article Subordination and Superordination on Schwarzian Derivatives
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 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 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 informationTHE FEKETE-SZEGÖ COEFFICIENT FUNCTIONAL FOR TRANSFORMS OF ANALYTIC FUNCTIONS. Communicated by Mohammad Sal Moslehian. 1.
Bulletin of the Iranian Mathematical Society Vol. 35 No. (009 ), pp 119-14. THE FEKETE-SZEGÖ COEFFICIENT FUNCTIONAL FOR TRANSFORMS OF ANALYTIC FUNCTIONS R.M. ALI, S.K. LEE, V. RAVICHANDRAN AND S. SUPRAMANIAM
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 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 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 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 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 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 informationResearch Article New Classes of Analytic Functions Involving Generalized Noor Integral Operator
Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008, Article ID 390435, 14 pages doi:10.1155/2008/390435 Research Article New Classes of Analytic Functions Involving Generalized
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 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 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 informationON A DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF NEW CLASS OF MEROMORPHIC FUNCTIONS
LE MATEMATICHE Vol. LXIX 2014) Fasc. I, pp. 259 274 doi: 10.4418/2014.69.1.20 ON A DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF NEW CLASS OF MEROMORPHIC FUNCTIONS ALI MUHAMMAD - MARJAN SAEED In this
More informationCoefficient Estimates for Bazilevič Ma-Minda Functions in the Space of Sigmoid Function
Malaya J. Mat. 43)206) 505 52 Coefficient Estimates for Bazilevič Ma-Minda Functions in the Space of Sigmoid Function Sunday Oluwafemi Olatunji a, and Emmanuel Jesuyon Dansu b a,b Department of Mathematical
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 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 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 informationCoefficient inequalities for certain subclasses Of p-valent functions
Coefficient inequalities for certain subclasses Of -valent functions R.B. Sharma and K. Saroja* Deartment of Mathematics, Kakatiya University, Warangal, Andhra Pradesh - 506009, India. rbsharma_005@yahoo.co.in
More informationSUBORDINATION RESULTS FOR A CERTAIN SUBCLASS OF NON-BAZILEVIC ANALYTIC FUNCTIONS DEFINED BY LINEAR OPERATOR
italian jornal of pre and applied mathematics n. 34 215 375 388) 375 SUBORDINATION RESULTS FOR A CERTAIN SUBCLASS OF NON-BAZILEVIC ANALYTIC FUNCTIONS DEFINED BY LINEAR OPERATOR Adnan G. Alamosh Maslina
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 informationResearch Article A Third-Order Differential Equation and Starlikeness of a Double Integral Operator
Abstract and Applied Analysis Volume 2, Article ID 9235, pages doi:.55/2/9235 Research Article A Third-Order Differential Equation and Starlikeness of a Double Integral Operator Rosihan M. Ali, See Keong
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 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 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 informationDifferential Subordination and Superordination Results for Certain Subclasses of Analytic Functions by the Technique of Admissible Functions
Filomat 28:10 (2014), 2009 2026 DOI 10.2298/FIL1410009J Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: htt://www.mf.ni.ac.rs/filomat Differential Subordination
More informationOn the improvement of Mocanu s conditions
Nunokawa et al. Journal of Inequalities Applications 13, 13:46 http://www.journalofinequalitiesapplications.com/content/13/1/46 R E S E A R C H Open Access On the improvement of Mocanu s conditions M Nunokawa
More informationResearch Article Some Starlikeness Criterions for Analytic Functions
Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010, Article ID 175369, 11 pages doi:10.1155/2010/175369 Research Article Some Starlikeness Criterions for Analytic Functions
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 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 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 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 informationA New Subclasses of Meromorphic p-valent Functions with Positive Coefficient Defined by Fractional Calculus Operators
Volume 119 No. 15 2018, 2447-2461 ISSN: 1314-3395 (on-line version) url: http://www.acadpubl.eu/hub/ http://www.acadpubl.eu/hub/ A New Subclasses of Meromorphic p-valent Functions with Positive Coefficient
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 informationA Certain Subclass of Multivalent Analytic Functions Defined by Fractional Calculus Operator
British Journal of Mathematics & Comuter Science 4(3): 43-45 4 SCIENCEDOMAIN international www.sciencedomain.org A Certain Subclass of Multivalent Analytic Functions Defined by Fractional Calculus Oerator
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 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 informationSufficient conditions for starlike functions associated with the lemniscate of Bernoulli
Kumar et al. Journal of Inequalities and Applications 2013, 2013:176 R E S E A R C H Open Access Sufficient conditions for starlike functions associated with the lemniscate of Bernoulli S Sivaprasad Kumar
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 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 informationA. Then p P( ) if and only if there exists w Ω such that p(z)= (z U). (1.4)
American International Journal of Research in Science, Technology, Engineering & Mathematics Available online at http://www.iasir.net ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629
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 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 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 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 informationResearch Article Subordination Results on Subclasses Concerning Sakaguchi Functions
Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009, Article ID 574014, 7 pages doi:10.1155/2009/574014 Research Article Subordination Results on Subclasses Concerning Sakaguchi
More informationOn Classes of Analytic Functions Associated by a Parametric Linear Operator in a Complex Domain
Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences 54 (3): 257 267 (207) Copyright Pakistan Academy of Sciences ISSN: 258-4245 (print), 258-4253 (online) Pakistan Academy
More informationSufficient conditions for certain subclasses of meromorphic p-valent functions
Bol. Soc. Paran. Mat. (3s.) v. 33 (015): 9 16. c SPM ISSN-175-1188 on line ISSN-0037871 in ress SPM: www.sm.uem.br/bsm doi:10.569/bsm.v33i.1919 Sufficient conditions for certain subclasses of meromorhic
More informationa n z n, z U.. (1) f(z) = z + n=2 n=2 a nz n and g(z) = z + (a 1n...a mn )z n,, z U. n=2 a(a + 1)b(b + 1) z 2 + c(c + 1) 2! +...
ISSN 1749-3889 (print), 1749-3897 (online) International Journal of Nonlinear Science Vol.13(2012) No.2,pp.153-157 Integral Operator Defined by Convolution Product of Hypergeometric Functions Maslina Darus,
More informationON CERTAIN SUBCLASSES OF UNIVALENT FUNCTIONS AND RADIUS PROPERTIES
ON CERTAIN SUBCLASSES OF UNIVALENT FUNCTIONS AND RADIUS PROPERTIES M. OBRADOVIĆ and S. PONNUSAMY Let S denote the class of normalied univalent functions f in the unit disk. One of the problems addressed
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 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 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 informationAn Integrodifferential Operator for Meromorphic Functions Associated with the Hurwitz-Lerch Zeta Function
Filomat 30:7 (2016), 2045 2057 DOI 10.2298/FIL1607045A Pulished y Faculty of Sciences Mathematics, University of Niš, Seria Availale at: http://www.pmf.ni.ac.rs/filomat An Integrodifferential Operator
More informationFișa de verificare a îndeplinirii standardelor minimale NOTĂ: În coloana "Publicat în ultimii 7 ani" se bifează cu X articolele din M recent
Universitatea din Oradea Facultatea de Științe, Departamentul de Matematică și Informatică Conf.univ.dr. OROS Georgia Irina Nr. Crt. Fișa de verificare a îndeplinirii standardelor minimale NOTĂ: În coloana
More informationA SUBORDINATION THEOREM WITH APPLICATIONS TO ANALYTIC FUNCTIONS
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 3 Issue 3(2011, Pages 1-8. A SUBORDINATION THEOREM WITH APPLICATIONS TO ANALYTIC FUNCTIONS (COMMUNICATED
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics APPLICATIONS OF DIFFERENTIAL SUBORDINATION TO CERTAIN SUBCLASSES OF MEROMORPHICALLY MULTIVALENT FUNCTIONS H.M. SRIVASTAVA AND J. PATEL Department
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 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 informationDifferential Subordinations and Harmonic Means
Bull. Malays. Math. Sci. Soc. (2015) 38:1243 1253 DOI 10.1007/s40840-014-0078-9 Differential Subordinations and Harmonic Means Stanisława Kanas Andreea-Elena Tudor eceived: 9 January 2014 / evised: 3 April
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 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 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 informationMajorization Properties for Subclass of Analytic p-valent Functions Defined by the Generalized Hypergeometric Function
Tamsui Oxford Journal of Information and Mathematical Sciences 284) 2012) 395-405 Aletheia University Majorization Properties for Subclass of Analytic p-valent Functions Defined by the Generalized Hypergeometric
More informationMalaya J. Mat. 4(1)(2016) 37-41
Malaya J. Mat. 4(1)(2016) 37-41 Certain coefficient inequalities for -valent functions Rahim Kargar a,, Ali Ebadian a and Janus Sokół b a Deartment of Mathematics, Payame Noor University, I. R. of Iran.
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 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 CERTAIN CLASSES OF UNIVALENT MEROMORPHIC FUNCTIONS ASSOCIATED WITH INTEGRAL OPERATORS
TWMS J. App. Eng. Math. V.4, No.1, 214, pp. 45-49. ON CERTAIN CLASSES OF UNIVALENT MEROMORPHIC FUNCTIONS ASSOCIATED WITH INTEGRAL OPERATORS F. GHANIM 1 Abstract. This paper illustrates how some inclusion
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 informationA Certain Subclass of Analytic Functions Defined by Means of Differential Subordination
Filomat 3:4 6), 3743 3757 DOI.98/FIL64743S Published by Faculty of Sciences Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat A Certain Subclass of Analytic Functions
More informationSUBORDINATION AND SUPERORDINATION FOR FUNCTIONS BASED ON DZIOK-SRIVASTAVA LINEAR OPERATOR
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 2, Issue 3(21), Pages 15-26. SUBORDINATION AND SUPERORDINATION FOR FUNCTIONS BASED ON DZIOK-SRIVASTAVA
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 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 informationSUBCLASS OF HARMONIC STARLIKE FUNCTIONS ASSOCIATED WITH SALAGEAN DERIVATIVE
LE MATEMATICHE Vol. LXIX (2014) Fasc. II, pp. 147 158 doi: 10.4418/2014.69.2.13 SUBCLASS OF HARMONIC STARLIKE FUNCTIONS ASSOCIATED WITH SALAGEAN DERIVATIVE H. E. DARWISH - A. Y. LASHIN - S. M. SOILEH The
More informationDifferential Sandwich Theorem for Multivalent Meromorphic Functions associated with the Liu-Srivastava Operator
KYUNGPOOK Math. J. 512011, 217-232 DOI 10.5666/KMJ.2011.51.2.217 Differential Sandwich Theorem for Multivalent Meromorhic Functions associated with the Liu-Srivastava Oerator Rosihan M. Ali, R. Chandrashekar
More informationn=2 AMS Subject Classification: 30C45. Keywords and phrases: Starlike functions, close-to-convex functions, differential subordination.
MATEMATIQKI VESNIK 58 (2006), 119 124 UDK 517.547 originalni nauqni rad research paper ON CETAIN NEW SUBCLASS OF CLOSE-TO-CONVEX FUNCTIONS Zhi-Gang Wang, Chun-Yi Gao and Shao-Mou Yuan Abstract. In the
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 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 informationResearch Article A New Class of Meromorphically Analytic Functions with Applications to the Generalized Hypergeometric Functions
Abstract and Applied Analysis Volume 20, Article ID 59405, 0 pages doi:0.55/20/59405 Research Article A New Class of Meromorphically Analytic Functions with Applications to the Generalized Hypergeometric
More informationSubclasses of Analytic Functions with Respect. to Symmetric and Conjugate Points
Theoretical Mathematics & Applications, vol.3, no.3, 2013, 1-11 ISSN: 1792-9687 (print), 1792-9709 (online) Scienpress Ltd, 2013 Subclasses of Analytic Functions with Respect to Symmetric and Conjugate
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 informationNEW SUBCLASS OF MULTIVALENT HYPERGEOMETRIC MEROMORPHIC FUNCTIONS
Kragujevac Journal of Mathematics Volume 42(1) (2018), Pages 83 95. NEW SUBCLASS OF MULTIVALENT HYPERGEOMETRIC MEROMORPHIC FUNCTIONS M. ALBEHBAH 1 AND M. DARUS 2 Abstract. In this aer, we introduce a new
More informationOn Certain Class of Meromorphically Multivalent Reciprocal Starlike Functions Associated with the Liu-Srivastava Operator Defined by Subordination
Filomat 8:9 014, 1965 198 DOI 10.98/FIL1409965M Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat On Certain Class of Meromorphically
More informationNOTE ON RADIUS PROBLEMS FOR CERTAIN CLASS OF ANALYTIC FUNCTIONS. We dedicate this paper to the 60th anniversary of Professor Y. Polatoglu.
NOTE ON RADIUS PROBLEMS FOR CERTAIN CLASS OF ANALYTIC FUNCTIONS Neslihan Uyanik 1, Shigeyoshi Owa 2 We dedicate this paper to the 60th anniversary of Professor Y. Polatoglu Abstract For analytic functions
More informationSubclasses of starlike functions associated with some hyperbola 1
General Mathematics Vol. 14, No. 2 2006, 31 42 Subclasses of starlike functions associated with some hyperbola 1 Mugur Acu Abstract In this paper we define some subclasses of starlike functions associated
More informationResearch Article Sufficient Conditions for Janowski Starlikeness
Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 2007, Article ID 62925, 7 pages doi:10.1155/2007/62925 Research Article Sufficient Conditions for Janowski
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 informationSUBCLASSES OF P-VALENT STARLIKE FUNCTIONS DEFINED BY USING CERTAIN FRACTIONAL DERIVATIVE OPERATOR
Sutra: International Journal of Mathematical Science Education Technomathematics Research Foundation Vol. 4 No. 1, pp. 17-32, 2011 SUBCLASSES OF P-VALENT STARLIKE FUNCTIONS DEFINED BY USING CERTAIN FRACTIONAL
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 informationAn Application of Wilf's Subordinating Factor Sequence on Certain Subclasses of Analytic Functions
International Journal of Applied Engineering Research ISS 0973-4562 Volume 3 umber 6 (208 pp. 2494-2500 An Application of Wilf's Subordinating Factor Sequence on Certain Subclasses of Analytic Functions
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 informationSome basic properties of certain subclasses of meromorphically starlike functions
Wang et al. Journal of Inequalities Applications 2014, 2014:29 R E S E A R C H Open Access Some basic properties of certain subclasses of meromorphically starlike functions Zhi-Gang Wang 1*, HM Srivastava
More informationarxiv: v1 [math.cv] 22 Apr 2009
arxiv:94.3457v [math.cv] 22 Apr 29 CERTAIN SUBCLASSES OF CONVEX FUNCTIONS WITH POSITIVE AND MISSING COEFFICIENTS BY USING A FIXED POINT SH. NAJAFZADEH, M. ESHAGHI GORDJI AND A. EBADIAN Abstract. By considering
More information