The Fekete-Szegö Theorem for a Certain Class of Analytic Functions (Teorem Fekete-Szegö Bagi Suatu Kelas Fungsi Analisis)
|
|
- Felix Jackson
- 6 years ago
- Views:
Transcription
1 Sains Malaysiana 40(4)(2011): The Fekete-Szegö Theorem for a Certain Class of Analytic Functions (Teorem Fekete-Szegö Bagi Suatu Kelas Fungsi Analisis) MA`MOUN HARAYZEH AL-ABBADI & MASLINA DARUS* ABSTRACT In this paper, we discuss a well known class studied y many authors including Ramesha et al Janteng, few to mention Next, we extend the class to a wider class of functions f denoted y u a, which are normalized univalent, in the open unit disk D={z: z <1} satisfying the condition: where g S * (),g(z) 0 is a normalized starlike function of order, for 0 < 1 For f u a we shall otain sharp upper ounds for the Fekete-Szegö functional a 3 µa 22 when µ is real Keywords: Close-to-convex functions; convex functions; Fekete- Szegö theorem; starlike functions; univalent functions ABSTRAK Dalam kertas kerja ini, kelas yang terkenal yang dikaji oleh ramai penulis akan diincangkan, termasuklah eerapa nama seperti Ramesha et al dan Janteng Seterusnya, kelas ini diperluaskan kepada kelas fungsi f dilamangkan oleh u a, yang ternormal dan univalen dalam cakera unit teruka D={z: z <1} memenuhi syarat: yang g S * (),g(z) 0 adalah fungsi ak-intang ternormal peringkat, (0 < 1) Untuk f u a atas atas teraik agi fungsian Fekete-Szegö a 3 µa 22 diperoleh apaila µ adalah nyata Kata kunci: Fungsi ak-intang; fungsi cemung; fungsi hampir cemung; fungsi univalen; teorem Fekete- Szegö INTRODUCTION AND DEFINITION Let S denotes the class of normalized analytic univalent functions f of the form: (1) a n is a complex numer z D = {z: z <1} A classical theorem of Fekete & Szegö (1933), states that for f S given y (1), (1987), Darus Thomas (1996, 2000), Irahim Darus (2001), Rahman Darus (2001), Darus (2002), Darus Tuneski (2003), Darus Hong (2004), Frasin Darus (2003) In particular, for f K e given y (1), Keogh Merkes (1969) showed that: for 0 μ 1 the inequality is sharp For the suclass of S, consisting of convex functions C, starlike functions S *, close-to-convex functions K Sharp upper ounds for the functional a 3 μa 22 have een studied y various authors, however we mention only few names here such as Keogh Merkes (1969), Koepf for each µ there is a function in K for which equality holds In this paper, we give an estimate for the same functional for the class u a defined as follows:
2 386 Definition 11: For 0 a<1 0 β<1, let the function f e analytic in D e given y (1) Then the function f u α β if only if there exist g S * (β) such that for z D (2) Here, S * (β) denotes the class of starlike functions of order β, that is g S * (β) if only if g is analytic in D, 2 3 = (p p 1 ) (1 β) (6) It also follows from (2) that α z 2 f" (z) + zf (z) = g(z) h(z) (7) where Re h(z) > 0, writing h(z) = 1 + c 1 z + c 2 z 2, where c 1, c 2,, are complex numers from (7), we have (3) Note that if the function g(z) in (2) is replaced y f (z), we get the definition of Ramesha et al (1995) However, the authors (Ramesha et al) did not define the inequality as in (3) The work of Ramesha et al (1995) has attracted many authors such as Oradovic Joshi (1998), Janteng (1999, 2006) Akarally (2001) We first state some preliminary lemmas, required for proving our result PRELIMINARY RESULTS Lemma 21: (Pommerenke 1975) Let h e analytic in D with Re h(z) > 0 e given y, h(z) = 1+c 1 z+c 2 z 2 +, for z D, then c n 2, where n 1, Lemma 22: (Darus & Thomas 1996) For 0 β<1, let g S *( β ) with g(z) = z + 2 z z 3 Then, for µ real And equating coefficients, gives 2(α + 1)a 2 = c (8) 3(2α + 1) a 3 = c c (9) The result now follows on using classical inequalities, p 1 2, p 2 2, c 1 2, c 2 2, applying the following inequalities, 2 2 (1 β) 3 (1 β) (3 2β), which follow from (5) (6) Now, we shall show our main result for the class u αβ MAIN RESULT Theorem 31: Let the function f e given y (1) elongs to the class u αβ Then, for 0 α < 1 0 β < 1, 3(2α + 1)(a + 1) 2 a 3 u a 22 3 µ 22 (1 β)max{1, 3 2β 4µ(1 β) } Next, we give our first result as follows: Lemma 23: Let the function f given y (1) elongs to the class u αβ Then (α + 1) a 2 2 β 3(2α + 1) a 3 (3 2β)(3 β) Proof Since g S * (β), it follows from (3) that zg (z) = [β + (1 β) p(z)] g(z) (4) For z β, with Re p(z) < 0 given y where p 1, p 2,, are complex numers Equating coefficients, we otain 2 (1 β), (5) Inequalities are sharp for all cases
3 387 Proof Write: From (8) (9), we have: A straightforward calculation, we find: Then we get: Now we have: Next, since x o 2, we get, the interval (12) (10) in the case From (10) gives: And hence, the result (12) completes the proof for the case: Now consider the first case for all We can see that the result is sharp y choosing: Having, c 2 = 2, p 1 = 2, p 2 = 2, 2 = 2(1 β) 3 = (3 2β) (1 β), sustituting in (10) to get the desired result Secondly, we consider the case: 2(α + 1) 2 3(2α + 1) μ 0, y applying the following inequalities, Write, 2 2(1 β), 3 (3 2 β) (1 β) Lemma 21 we get: Now we say that, y using the inequality we otain the following: (11) = φ(x), say, with x = c 1 Elementary calculation indicates that the function φ attains its maximum value at:
4 388 This completes the proof for this case Here, in order to find the upper ound for: (13) 2 A straightforward calculation shows that the function ψ(x) attains asolute maximum value in the interval [0, 2] at x o = 0 And after some simplifications, we conclude that ψ(x), 3 β, at x o = 0 And therefore, we get the result: (14) we use the previous result of (12), which is already proved for:, When sustitute in last result (12) gives the following: Hence completing the proof for the particular case After that, we have to make sure that the result is sharp for this case Upon choosing, c 1 = c 2 = p 2, 2 = 2(1 β) 3 = (3 2β) (1 β) in (10) we get the required result Next we consider the case for all: The result is sharp on choosing c 1 = 0, p 2 = 2, c 2 = 2, 2 = 0 3 = 1 β sustituting in (10), doing a simple calculation, we shall get the desired equality Finally, consider: Consider the case: Write: First, we take the case: We start from, (11) y sustituting: Now we say that, y using the inequality we otain the following: We get: Hence the proof is complete for this case Here, (15) = ψ(x), say, with x = c 1 Assume our maximum value, otained in x o [0, 2] ut through calculation it happens on so it is out of the interval, so it contradicts the assumption Then the maximum value may occur on the oundary x o = 0 or we used the last result (14) already proven for The result is sharp on choosing c 2 = 2i, c 2 = p 2 = -2, 2 = 2i(1 β) 3 (3 2β) (β 1) sustituting in (10)
5 389 ACKNOWLEDGEMENTs This work is supported y UKM-ST-06-FRGS , Malaysia The authors would like to thank referees for some comments that improved the paper REFERENCES Akarally, A 2001 Beerapa Masalah Pekali dan Suordinasi untuk Fungsi Bak Bintang MSc thesis, Universiti Keangsaan Malaysia, Malaysia Darus, M & Thomas, DK 1996 On the Fekete-Szegö theorem for close-to-convex functions Math Japonica 44(3): Darus, M & Thomas, DK 2000 The Fekete-Szegö prolem for strongly close-to-convex functions Scientiae Mathematicae 3(2): Darus, M 2002 The Fekete-Szegö prolems for close-to-convex functions of the class K hs (α, β) Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis 18(1): Darus, M & Tuneski, N 2003 On the Fekete-Szegö prolem for generalized close-to-convex functions InterMath Jour 4(6): Darus, M & Hong, NC 2004 The Fekete-Szegö prolem for strongly close-to-convex functions with Hadamard product Far East J Math Sci (FJMS) 15(1): 1-7 Fekete, M & Szegö, G 1933 Eine Bermerkung üer ungerade schlichte function J Lond Math Soc 8: Frasin, BA & Darus, M 2003 On the Fekete- Szegö using the Hadamard product Internat Math J 3(12): Irahim, A & Darus, M 2001 The Fekete-Szegö theorem for close-to-convex functions: To determine the upper ounds Jour Inst Math CompSci (MathSer) 14(3): Janteng, A 2006 Assortment of Prolems for Certain Classes of Analytic Functions PhD thesis, University of Malaya, KL Malaysia Janteng, A 1999 Beerapa Masalah untuk Fungsi Bak Bintang MSc thesis, Universiti Keangsaan Malaysia, Malaysia Keogh, FR & Merkes, EP 1969 A coefficient inequality for certain classes of analytic functions Proc Amer Math Soc 20: 8-12 Koepf, W 1987 On the Fekete-Szegö prolem for close-toconvex functions Proc Amer Math Soc 101: Oradovic, M & Joshi, SB 1998 On certain classes of strongly starlike functions Taiwanese J Math 2: Pommerenke, CH 1975 Univalent Functions Göttingen: Venhoeck Ruprecht Ramesha, C Kumar, S & Padmanahan, KS 1995 A sufficient condition for starlikeness Chinese J Math 23: Rahman, KA & Darus, M 2001 The Fekete-Szegö prolems for close-to-convex functions of the class K hs (α, β) Jour Inst Math Comp Sci(Math Ser) 14(3): School of Mathematical Sciences Faculty of Science Technology Universiti Keangsaan Malaysia Bangi, Selangor DE Malaysia *Corresponding authors; maslina@ukmmy Received: 9 Decemer 2009 Accepted: 18 July 2010
Applied Mathematics Letters
Applied Mathematics Letters 3 (00) 777 78 Contents lists availale at ScienceDirect Applied Mathematics Letters journal homepage: wwwelseviercom/locate/aml Fekete Szegö prolem for starlike convex functions
More informationCoefficient Bounds for Certain Subclasses of Analytic Function Involving Hadamard Products
Mathematica Aeterna, Vol. 4, 2014, no. 4, 403-409 Coefficient Bounds for Certain Subclasses of Analytic Function Involving Hadamard Products V.G. Shanthi Department of Mathematics S.D.N.B. Vaishnav College
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 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 informationACTA UNIVERSITATIS APULENSIS No 18/2009 SOME SUBCLASS OF ANALYTIC FUNCTIONS. Firas Ghanim and Maslina Darus
ACTA UNIVERSITATIS APULENSIS No 18/2009 SOME SUBCLASS OF ANALYTIC FUNCTIONS Firas Ghanim and Maslina Darus Abstract. In this paper we introduce a new class M (α, β, γ, A, λ) consisting analytic and univalent
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 informationSecond Hankel determinant for the class of Bazilevic functions
Stud. Univ. Babeş-Bolyai Math. 60(2015), No. 3, 413 420 Second Hankel determinant for the class of Bazilevic functions D. Vamshee Krishna and T. RamReddy Abstract. The objective of this paper is to obtain
More informationOn a class of analytic functions related to Hadamard products
General Mathematics Vol. 15, Nr. 2 3(2007), 118-131 On a class of analytic functions related to Hadamard products Maslina Darus Abstract In this paper, we introduce a new class of analytic functions which
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 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 informationCONVOLUTION AND COEFFICIENT PROBLEMS FOR MULTIVALENT FUNCTIONS DEFINED BY SUBORDINATION SHAMANI A/P SUPRAMANIAM UNIVERSITI SAINS MALAYSIA
CONVOLUTION AND COEFFICIENT PROBLEMS FOR MULTIVALENT FUNCTIONS DEFINED BY SUBORDINATION SHAMANI A/P SUPRAMANIAM UNIVERSITI SAINS MALAYSIA 009 CONVOLUTION AND COEFFICIENT PROBLEMS FOR MULTIVALENT FUNCTIONS
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 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 informationSECOND HANKEL DETERMINANT FOR A CERTAIN SUBCLASS OF ANALYTIC AND BI-UNIVALENT FUNCTIONS
TWMS J Pure Appl Math V7, N, 06, pp85-99 SECOND HANKEL DETERMINANT FOR A CERTAIN SUBCLASS OF ANALYTIC AND BI-UNIVALENT FUNCTIONS BA FRASIN, K VIJAYA, M KASTHURI Abstract In the present paper, we consider
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 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 informationCOEFFICIENT INEQUALITY FOR CERTAIN SUBCLASS OF ANALYTIC FUNCTIONS
Armenian Journal of Mathematics Volume 4, Number 2, 2012, 98 105 COEFFICIENT INEQUALITY FOR CERTAIN SUBCLASS OF ANALYTIC FUNCTIONS D Vamshee Krishna* and T Ramreddy** * Department of Mathematics, School
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 informationTHIRD HANKEL DETERMINANT FOR THE INVERSE OF RECIPROCAL OF BOUNDED TURNING FUNCTIONS HAS A POSITIVE REAL PART OF ORDER ALPHA
ISSN 074-1871 Уфимский математический журнал. Том 9. т (017). С. 11-11. THIRD HANKEL DETERMINANT FOR THE INVERSE OF RECIPROCAL OF BOUNDED TURNING FUNCTIONS HAS A POSITIVE REAL PART OF ORDER ALPHA B. VENKATESWARLU,
More informationCOEFFICIENT INEQUALITY FOR CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS
NEW ZEALAND JOURNAL OF MATHEMATICS Volume 42 (2012), 217-228 COEFFICIENT INEQUALITY FOR CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS D. VAMSHEE KRISHNA 1 and T. RAMREDDY (Received 12 December, 2012) Abstract.
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 informationCONVOLUTION, COEFFICIENT AND RADIUS PROBLEMS OF CERTAIN UNIVALENT FUNCTIONS MAISARAH BT. HAJI MOHD UNIVERSITI SAINS MALAYSIA
CONVOLUTION, COEFFICIENT AND RADIUS PROBLEMS OF CERTAIN UNIVALENT FUNCTIONS MAISARAH BT. HAJI MOHD UNIVERSITI SAINS MALAYSIA 2009 CONVOLUTION, COEFFICIENT AND RADIUS PROBLEMS OF CERTAIN UNIVALENT FUNCTIONS
More informationSECOND HANKEL DETERMINANT PROBLEM FOR SOME ANALYTIC FUNCTION CLASSES WITH CONNECTED K-FIBONACCI NUMBERS
Ata Universitatis Apulensis ISSN: 15-539 http://www.uab.ro/auajournal/ No. 5/01 pp. 161-17 doi: 10.1711/j.aua.01.5.11 SECOND HANKEL DETERMINANT PROBLEM FOR SOME ANALYTIC FUNCTION CLASSES WITH CONNECTED
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 informationarxiv: v1 [math.cv] 28 Mar 2017
On third Hankel determinants for subclasses of analytic functions and close-to-convex harmonic mappings arxiv:703.09485v math.cv] 28 Mar 207 Yong Sun, Zhi-Gang Wang 2 and Antti Rasila 3 School of Science,
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 informationHarmonic Mappings for which Second Dilatation is Janowski Functions
Mathematica Aeterna, Vol. 3, 2013, no. 8, 617-624 Harmonic Mappings for which Second Dilatation is Janowski Functions Emel Yavuz Duman İstanbul Kültür University Department of Mathematics and Computer
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 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 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 informationSOME PROPERTIES OF A SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY A GENERALIZED SRIVASTAVA-ATTIYA OPERATOR. Nagat. M. Mustafa and Maslina Darus
FACTA UNIVERSITATIS NIŠ) Ser. Math. Inform. Vol. 27 No 3 2012), 309 320 SOME PROPERTIES OF A SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY A GENERALIZED SRIVASTAVA-ATTIYA OPERATOR Nagat. M. Mustafa and Maslina
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 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 informationSubclass of Meromorphic Functions with Positive Coefficients Defined by Frasin and Darus Operator
Int. J. Open Problems Complex Analysis, Vol. 8, No. 1, March 2016 ISSN 2074-2827; Copyright c ICSRS Publication, 2016 www.i-csrs.org Subclass of Meromorphic Functions with Positive Coefficients Defined
More informationABSTRACT. Keywords: Contractive condition; fixed-point; partially ordered metric space ABSTRAK
Sains Malaysiana 46(8)(2017): 1341 1346 http://dxdoiorg/1017576/jsm-2017-4608-21 The Existence of ϒ-fixed Point for the Multidimensional Nonlinear Mappings Satisfying (ψ, θ, ϕ)-weak Contractive Conditions
More informationTHE U -RADIUS AND HANKEL DETERMINANT FOR ANALYTIC FUNCTIONS, AND PRODUCT OF LOGHARMONIC MAPPINGS NAJLA MOHAMMED ALARIFI UNIVERSITI SAINS MALAYSIA
THE U -RADIUS AND HANKEL DETERMINANT FOR ANALYTIC FUNCTIONS, AND PRODUCT OF LOGHARMONIC MAPPINGS NAJLA MOHAMMED ALARIFI UNIVERSITI SAINS MALAYSIA 07 THE U -RADIUS AND HANKEL DETERMINANT FOR ANALYTIC FUNCTIONS,
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 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 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 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 informationBounds on Hankel determinant for starlike and convex functions with respect to symmetric points
PURE MATHEMATICS RESEARCH ARTICLE Bounds on Hankel determinant for starlike convex functions with respect to symmetric points Ambuj K. Mishra 1, Jugal K. Prajapat * Sudhana Maharana Received: 07 November
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 informationarxiv: v1 [math.cv] 11 Aug 2017
CONSTRUCTION OF TOEPLITZ MATRICES WHOSE ELEMENTS ARE THE COEFFICIENTS OF UNIVALENT FUNCTIONS ASSOCIATED WITH -DERIVATIVE OPERATOR arxiv:1708.03600v1 [math.cv] 11 Aug 017 NANJUNDAN MAGESH 1, ŞAHSENE ALTINKAYA,,
More informationCONCAVE MEROMORPHIC FUNCTIONS INVOLVING CONSTRUCTED OPERATORS. M. Al-Kaseasbeh, M. Darus
Acta Universitatis Apulensis ISSN: 582-5329 http://www.uab.ro/auajournal/ doi: No. 52/207 pp. -9 0.74/j.aua.207.52.02 CONCAVE MEROMORPHIC FUNCTIONS INVOLVING CONSTRUCTED OPERATORS M. Al-Kaseasbeh, M. Darus
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 informationBIII/. Malaysinn Math. Sc. Soc. (Second Series) 26 (2003) Coefficients of the Inverse of Strongly Starlike Functions. ROSlHAN M.
BULLETIN of the MALAYSIAN MATHEMATICAL SCIENCES SOCIETY BIII/. Malaysinn Math. Sc. Soc. (Second Series) 26 (2003) 63-71 Coefficients of the Inverse of Strongly Starlike Functions ROSlHAN M. ALI School
More informationCoefficient bounds for some subclasses of p-valently starlike functions
doi: 0.2478/v0062-02-0032-y ANNALES UNIVERSITATIS MARIAE CURIE-SKŁODOWSKA LUBLIN POLONIA VOL. LXVII, NO. 2, 203 SECTIO A 65 78 C. SELVARAJ, O. S. BABU G. MURUGUSUNDARAMOORTHY Coefficient bounds for some
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 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 informationOn subclasses of n-p-valent prestarlike functions of order beta and type gamma Author(s): [ 1 ] [ 1 ] [ 1 ] Address Abstract KeyWords
On subclasses of n-p-valent prestarlike functions of order beta and type gamma Elrifai, EA (Elrifai, E. A.) [ 1 ] ; Darwish, HE (Darwish, H. E.) [ 1 ] ; Ahmed, AR (Ahmed, A. R.) [ 1 ] E-mail Address: Rifai@mans.edu.eg;
More informationFABER POLYNOMIAL COEFFICIENT ESTIMATES FOR A NEW SUBCLASS OF MEROMORPHIC BI-UNIVALENT FUNCTIONS ADNAN GHAZY ALAMOUSH, MASLINA DARUS
Available online at http://scik.org Adv. Inequal. Appl. 216, 216:3 ISSN: 25-7461 FABER POLYNOMIAL COEFFICIENT ESTIMATES FOR A NEW SUBCLASS OF MEROMORPHIC BI-UNIVALENT FUNCTIONS ADNAN GHAZY ALAMOUSH, MASLINA
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 informationCesáro partial sums of certain analytic functions
JIA_30_edited [0/06 19:18] 1/8 Cesáro partial sums of certain analytic functions 1 abha W Ibrahim and Maslina Darus 1 Institute of Mathematical Sciences, Universiti Malaya, 50603 Kuala Lumpur, Malaysia
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 informationCoefficient Inequalities of a Subclass of Starlike Functions Involving q - Differential Operator
Advances in Analysis, Vol. 3, No., April 018 https://dx.doi.org/10.606/aan.018.300 73 Coefficient Inequalities of a Subclass of Starlike Functions Involving q - Differential Operator K. R. Karthikeyan
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 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 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 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 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 informationHardy s Inequality for Functions of Several Complex Variables (Ketidaksamaan Hardy untuk Fungsi Beberapa Pemboleh Ubah Kompleks)
Sains Malaysiana 46(9)(2017): 1355 1359 http://dxdoiorg/1017576/jsm-2017-4609-01 Hardy s Inequality for Functions of Several Complex Variables (Ketidaksamaan Hardy untuk Fungsi Beberapa Pemboleh Ubah Kompleks)
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 informationSTARLIKENESS OF CERTAIN INTEGRAL OPERATORS AND PROPERTIES OF A SUBCLASS OF CLOSE-TO-CONVEX FUNCTIONS CHUNG YAO LIANG UNIVERSITI SAINS MALAYSIA
STARLIKENESS OF CERTAIN INTEGRAL OPERATORS AND PROPERTIES OF A SUBCLASS OF CLOSE-TO-CONVEX FUNCTIONS CHUNG YAO LIANG UNIVERSITI SAINS MALAYSIA 217 STARLIKENESS OF CERTAIN INTEGRAL OPERATORS AND PROPERTIES
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 informationOn a new class of (j, i)-symmetric function on conic regions
Available online at wwwisr-publicationscom/jnsa J Nonlinear Sci Appl 10 (2017) 4628 4637 Research Article Journal Homepage: wwwtjnsacom - wwwisr-publicationscom/jnsa On a new class of (j i)-symmetric function
More informationJordan Journal of Mathematics and Statistics (JJMS) 4(2), 2011, pp ON SOME PROPERTIES FOR NEW GENERALIZED DERIVATIVE OPERATOR. 1.
Jordan Journal of Mathematics and Statistics JJMS) 42), 2011, pp.91-101 ON SOME PROPERTIES FOR NEW GENERALIZED DERIVATIVE OPERATOR AISHA AHMED AMER 1) AND 2) MASLINA DARUS Abstract. Motiated by many well-known
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 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 informationStarlike Functions of Complex Order
Applied Mathematical Sciences, Vol. 3, 2009, no. 12, 557-564 Starlike Functions of Complex Order Aini Janteng School of Science and Technology Universiti Malaysia Sabah, Locked Bag No. 2073 88999 Kota
More informationConvolutions of Certain Analytic Functions
Proceedings of the ICM2010 Satellite Conference International Workshop on Harmonic and Quasiconformal Mappings (HQM2010) Editors: D. Minda, S. Ponnusamy, and N. Shanmugalingam J. Analysis Volume 18 (2010),
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 informationABSTRACT. Keywords: Abstract characterization; conditional expectation operator; measurable section ABSTRAK
Sains Malaysiana 46(1)(2017): 175 179 http://dxdoiorg/1017576/jsm-2017-4601-22 Abstract Characterization of a Conditional Expectation Operator on the Space of Measurable Sections (Pencirian Abstrak Bagi
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 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 informationCertain subclasses of uniformly convex functions and corresponding class of starlike functions
Malaya Journal of Matematik 1(1)(2013) 18 26 Certain subclasses of uniformly convex functions and corresponding class of starlike functions N Magesh, a, and V Prameela b a PG and Research Department of
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 informationarxiv: v3 [math.cv] 11 Aug 2014
File: SahSha-arXiv_Aug2014.tex, printed: 27-7-2018, 3.19 ON MAXIMAL AREA INTEGRAL PROBLEM FOR ANALYTIC FUNCTIONS IN THE STARLIKE FAMILY S. K. SAHOO AND N. L. SHARMA arxiv:1405.0469v3 [math.cv] 11 Aug 2014
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 informationA NEW SUBCLASS OF MEROMORPHIC FUNCTION WITH POSITIVE COEFFICIENTS
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 3 Issue 32010), Pages 109-121. A NEW SUBCLASS OF MEROMORPHIC FUNCTION WITH POSITIVE COEFFICIENTS S.
More informationOn close-to-convex functions satisfying a differential inequality
Stud. Univ. Babeş-Bolyai Math. 60(2015), No. 4, 561 565 On close-to-convex functions satisfying a differential inequality Sukhwinder Singh Billing Abstract. Let C α(β) denote the class of normalized functions
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 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 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 informationFekete-Szegö Inequality for Certain Classes of Analytic Functions Associated with Srivastava-Attiya Integral Operator
Applied Mathematical Sciences, Vol. 9, 015, no. 68, 3357-3369 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ams.015.543 Fekete-Szegö Inequality for Certain Classes of Analytic Functions Associated
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 informationResearch Article Some Properties of Certain Integral Operators on New Subclasses of Analytic Functions with Complex Order
Alied Mathematics Volume 2012, Article ID 161436, 9 ages doi:10.1155/2012/161436 esearch Article Some Proerties of Certain Integral Oerators on New Subclasses of Analytic Functions with Comlex Order Aabed
More informationMeromorphic Starlike Functions with Alternating and Missing Coefficients 1
General Mathematics Vol. 14, No. 4 (2006), 113 126 Meromorphic Starlike Functions with Alternating and Missing Coefficients 1 M. Darus, S. B. Joshi and N. D. Sangle In memoriam of Associate Professor Ph.
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 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 informationOn Quasi-Hadamard Product of Certain Classes of Analytic Functions
Bulletin of Mathematical analysis Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 1, Issue 2, (2009), Pages 36-46 On Quasi-Hadamard Product of Certain Classes of Analytic Functions Wei-Ping
More informationSubclasses of Analytic Functions. Involving the Hurwitz-Lerch Zeta Function
International Mathematical Forum, Vol. 6, 211, no. 52, 2573-2586 Suclasses of Analytic Functions Involving the Hurwitz-Lerch Zeta Function Shigeyoshi Owa Department of Mathematics Kinki University Higashi-Osaka,
More informationCoefficient Inequalities of Second Hankel Determinants for Some Classes of Bi-Univalent Functions
mathematics Article Coefficient Inequalities of Second Hankel Determinants for Some Classes of Bi-Univalent Functions Rayaprolu Bharavi Sharma Kalikota Rajya Laxmi, * Department of Mathematics, Kakatiya
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 informationarxiv: v1 [math.cv] 1 Nov 2017
arxiv:7.0074v [math.cv] Nov 07 The Fekete Szegö Coefficient Inequality For a New Class of m-fold Symmetric Bi-Univalent Functions Satisfying Subordination Condition Arzu Akgül Department of Mathematics,
More informationSains Malaysiana 40(2)(2011):
Sains na 40(2)(2011): 191 196 Improvement on the Innovational Outlier Detection Procedure in a Bilinear Model (Pembaikan Prosedur Pengesanan Nilai Sisihan Inovasi dalam Model Bilinear) I.B. Mohamed*, M.I.
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 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 informationOn the Second Hankel Determinant for the kth-root Transform of Analytic Functions
Filomat 3: 07 7 5 DOI 098/FIL707A Published by Faculty of Sciences and Mathematics University of Niš Serbia Available at: http://wwwpmfniacrs/filomat On the Second Hankel Determinant for the kth-root Transform
More informationCoefficient bounds for p-valent functions
Alied Mathematics and Comutation 7 (2007) 35 46 www.elsevier.com/locate/amc Coefficient bounds for -valent functions Rosihan M. Ali *, V. Ravichandran, N. Seenivasagan School of Mathematical Sciences,
More information