Differential Subordinations and Harmonic Means
|
|
- Harvey Garrett
- 6 years ago
- Views:
Transcription
1 Bull. Malays. Math. Sci. Soc. (2015) 38: DOI /s Differential Subordinations and Harmonic Means Stanisława Kanas Andreea-Elena Tudor eceived: 9 January 2014 / evised: 3 April 2014 / Published online: 22 January 2015 Malaysian Mathematical Sciences Society and Universiti Sains Malaysia 2015 Abstract The aim of a study of the presented paper is the differential subordination involving harmonic means of the expressions p(), p() + p (), and p() + p () p() when p is an analytic function in the unit disk, such that p(0) 1, p() 1. Several applications in the geometric functions theory are given. Keywords Univalent functions Subordination Differential subordination Harmonic means Mathematics Subject Classification Primary 31A05 Secondary 30C45 1 Introduction The harmonic mean, known also as the subcontrary mean, is one of several kinds of average, and is the special case power mean. It is used for the situations when the average of rates is desired and has several applications in geometry, trigonometry, probabilistics and statistics, algebra, physics, finance, computer science, etc. The harmonic mean is one of the Pythagorean means, along with the arithmetic and the geometric mean, and is no greater than either of them. The harmonic mean H of Communicated by V. avichandran. S. Kanas (B) University of esow, ul. S. Pigonia 1, esow, Poland skanas@ur.edu.pl A.-E. Tudor Babeş-Bolyai University, 1 Kogălniceanu Street, Cluj-Napoca, omania tudor_andreea_elena@yahoo.com
2 1244 S. Kanas, A.-E. Tudor the positive real numbers x 1, x 2,...,x n is defined to be the reciprocal of the arithmetic mean of the reciprocals of x 1, x 2,...,x n H ( 1 n n x k1 k ) 1 1. (1.1) For the special case of just two numbers x 1 and x 2, the harmonic mean can be written H 2x 1x 2 x 1 + x 2. In this special case, the harmonic mean is related to the arithmetic mean A x 1 + x 2, and the geometric mean G x 1 x 2, 2 by H G2 A,orG AH meaning the two numbers geometric mean equals the geometric mean of their arithmetic and harmonic means. Several concepts of the classes involving arithmetic and geometric means were appeared in the literature (see e.g. 1 9,11 14,16,17], for the extensive studies, we refer to the Miller and Mocanu monograph 10]). The purpose of this paper is to study the harmonic mean, as a supplementary to the well-known arithmetics and geometric Pythagorean means. In addition, a new mean brings along a wide range of new possibilities for exploiting harmonic ideas in connection of several quantities or functionals in the geometric function theory. In order to prove our main results, we introduce some fundamental notions and notations. Let A be the class of all analytic functions f in the open unit disk D { C : < 1}, oftheform: + a k k. (1.2) If f and g are two functions analytic in D, we say that f is subordinate to g, written as f g or g(), if there exists a Schwar function ω (i.e., analytic in D, with ω(0) 0 and ω() < 1, for all D) such that g(ω()), D. Furthermore, if g is univalent in D, then we have the following equivalence: k2 g() f (0) g(0) and f (D) g(d). Definition , p. 21] Denote by Q the set of functions q that are analytic and injective on D \ E(q), where E(q) { } ζ D : lim q(), ζ
3 Differential Subordinations and Harmonic Means 1245 such that q (ζ ) 0forζ D \ E(q). If q Q then q(d) is a simply connected domain. In order to prove our main results, we will need the following lemma: Lemma , p. 24] Let q Q, with q(0) a, and let p() a + a n n + be analytic in D with p() a and n 1. If p is not subordinate to q, then there exist points 0 r 0 e iθ 0 D and ζ 0 D \ E(q) and an m n 1 for which p(d r0 ) q(d), (1) p q(ζ 0 ), (2) 0 p mζ 0 q (ζ 0 ), (3) 0 p ζ0 q (ζ 0 ) p + 1 m q (ζ 0 ) ] Harmonic Mean Let p() 1 + a 1 + be analytic in D with p() 1. Then p() + p (), p() + has the same normaliation and play an important role in the theory of differential p () p() subordination. Let f A and set p(). Then p() + p () f (), and if p() f (), then p()+ p () p() 1+ f () f (). Extremal properties of such expressions, as well as several relations, were frequently considered in the theory of univalent functions. In this section, we study the differential subordination involving harmonic means of such expressions, and present some applications in the geometric functions theory. Theorem 2.1 Let p() 1 + a 1 + be analytic in D with p() 1. Then Proof Let { 2p() p() + p () ] } 2p() + p > 0 p() >0. (2.1) () q() q 1 +, (2.2) with q(d) {w :w>0}, q(0) 1, E(q) {1} and q Q. Then, we can rewrite the condition (2.1) as { 2p() p() + p () ] } 2p() + p > 0 p() q(). () Suppose that p() q().then, from Lemma 1.1, there exist a point 0 D and a point ζ 0 D \ {1} such that p q(ζ 0 ) and p() >0 for all D 0.This implies that p 0, therefore we can choose p of the form p : ix,
4 1246 S. Kanas, A.-E. Tudor where x is a real number. Due to symmetry, it is sufficient to consider only the case where x > 0. We have ζ 0 q 1 (p) p( 0) 1 p + 1, then 0 p mζ 0 q (ζ 0 ) m(x 2 + 1)/2 : y, where y < 0. Thus, we obtain: { 2p(0 ) p + 0 p ] } ] 2ix(ix + y) 2p + 0 p 2ix + y 2x2 y 4x 2 + y 2 < 0. This contradicts the hypothesis of the theorem, therefore p q and the proof of Theorem 2.1 is complete. emark 1 We only note that the expression of the left hand side of (2.1) isofthe harmonic form of two elements x 1 p() and x 2 p() + p ()( D). Setting p() in the previous theorem, we obtain the following corollary: Corollary 2.1 Let + a be analytic in D. Then 2 f () () + f > 0 f > 0. () Theorem 2.2 Let p() 1 + a 1 + be analytic in D with p() 1. Then 2p() + 2p ] () 1 + p 2 () + p()p > 0 p() >0. () Proof Following the same steps as in the proof of Theorem 2.1, setting p ix, x > 0 and 0 p y, y < 0, we obtain: 2p p ] 1 + p pp ] 2ix + 2y 1 x 2 + ixy 2y (1 x 2 ) 2 + x 2 y 2 < 0, which completes the proof. Setting p() we obtain Corollary 2.2 Let + a be analytic in D. Then 2 f () + f > 0 > 0. ()
5 Differential Subordinations and Harmonic Means 1247 Theorem 2.3 Let p() 1 + a 1 + be analytic in D with p() 1. Then 2 p() + p () p() 2 + p () p 2 () ] > 0 p() >0. Proof We only need to show that p q, where q is given by (2.2). As in the proof of Theorem 2.1, there exist a point 0 D such that p ix, x > 0 and 0 p y, y < 0. Therefore, we have 2 p + 0 p p p p 2 ] ( 2 ix + y ix 2 y x ) 0 < 0. and the proof of Theorem 2.3 is completed. Setting p() f () we obtain Corollary 2.3 Let + a be analytic in D. Then 2 f () ] 1 + f () f () 1 + f () + f () f () > 0 f () > 0. Theorem 2.4 Let p() 1 + a 1 + be analytic in D with p() 1. Then ] 2 p() + p () p() 1 + p 2 () + p > 0 p() >0. () Proof As in the proof of Theorem 2.1, there exist a point 0 in D such that p ix, x > 0 and 0 p y, y < 0. We have: 2 p + 0 p ] p 1 + p p ( 2 ix + y ix ) 1 x 2 + y 0, which completes the proof. Setting p() f () we obtain
6 1248 S. Kanas, A.-E. Tudor Corollary 2.4 Let + a be analytic in D. Then 2 f 1 + f () () f () 1 + f () + f () f () ] > 0 f () > 0. Theorem 2.5 Let p() 1 + a 1 + a be analytic in D with p() 1, and let 0 < M < 1 3. Then 2p() p() + p () ] 2p() + p 1 < M p() 1 < M. (2.3) () Proof Let q() 1 + M, (2.4) with q(d) {w : w 1 < M}, q(0) 1, E(q) and q Q. Then, the condition (2.3) can be rewritten as 2p() p() + p () ] 2p() + p 1 < M p() q(). () Suppose that p() q().then, from Lemma 1.1, there exist 0 D, ζ 0 D and m 1 such that p q(ζ 0 ) and p 1 < M for all D 0. This implies that p 1 q(ζ 0 ) 1 M, therefore we can choose p of the form p : 1 + Me iθ, where θ is a real number. We have then ζ 0 q 1 (p) p 1] /M, 0 p mζ 0 q (ζ 0 ) mme iθ, m 1. We can write: 2p p+ 0 p ] 2p+ 0 p 1 2p 2 + 2p 0 p 2p 0 p 2p + 0 p 2Me iθ + 2M 2 e 2iθ + mme iθ + 2mM 2 e 2iθ 2 + (2 + m)me iθ Me iθ 1 + m(1 + Meiθ ) 2 + (2 + m)me iθ M 1 + m(1 + Meiθ ) 2 + (2 + m)me iθ.
7 Differential Subordinations and Harmonic Means 1249 In order to obtain the contradiction it suffices to show that the last expression is greater or equal to M that is equivalent to the fact 1 + m(1 + Meiθ ) 2 + (2 + m)me iθ 1 or 2 + m + 2(m + 1)Me iθ (2 + m)me iθ 2. The last inequality holds by virtue of the inequality M 2 (3m+4)+4(2+m)M cos θ + m + 4 M 2 (3m + 4) 4(2 + m)m + m or ( (3m + 4)(M 1) M 4 + m ) m Since M does not exceed 1 3 the above expression is positive for every m 1. This contradicts the hypothesis of the theorem, therefore p q and the proof of Theorem 2.5 is complete. Let p(). Then the previous theorem reduce to the following corollary: Corollary 2.5 Let + a be analytic in D, and let 0 < M < 1. Then 2 f () 2 + f () 1 < M 1 < M. For the case, when p() f (), the Theorem 2.5 gives Corollary 2.6 Let + a be analytic in D, and let 0 < M < 1. Then 2( f () + f ()) f () < M f () 1 < M. f () Also, letting p() f () in Theorem 2.5, we conclude:
8 1250 S. Kanas, A.-E. Tudor Corollary 2.7 Let + a be analytic in D, and let 0 < M < 1. Then 2 f () ( ) 2 + f () f () f () 3 + f () f () f () 1 < M f () 1 < M. Theorem 2.6 Let p() 1 + a 1 + be analytic in D with p() 1 and let γ (0, 1]. Then 2p() p() + p () ] 2p() + p () <γπ 2 p() <γπ 2. (2.5) Proof Let q() ( ) 1 + γ 1 + q 1 +, (2.6) 1 with q(d) { w : w <γ π 2 }, q(0) 1, E(q) {1}, and q Q. Then, the condition (2.5) can be rewritten as 2p() p() + p () ] 2p() + p () <γπ 2 p() q(). Suppose that p() q().then, from Lemma 1.1, there exist 0 D, ζ 0 D \ {1} and m 1 such that p q(ζ 0 ) and 0 p mζ 0 q (ζ 0 ). This implies that p q(ζ 0 ) : (ix) γ x γ e γ π 2 i, (2.7) where x is a real number. Due to symmetry, it is sufficient to consider only the case where x > 0. We have and therefore we obtain ζ 0 q 1 (p) p( γ 0) 1 1, p γ ( x 0 p mζ 0 q (ζ 0 ) mγ x γ 2 ) + 1 e π 2 (γ +1)i. (2.8) 2x
9 Differential Subordinations and Harmonic Means 1251 Taking into consideration (2.7) and (2.8),we have 2p( 0) p(0 ) + 0 p ] 2p p ] 2p + 0 p p p p p p( p + 0 ) p p γ π 1 + ui ui γ π 2 + arctan u 2 + u 2 γ π 2, where ( x 2 ) + 1 u mγ > 0. 2x This contradicts the hypothesis of the theorem, therefore p q and the proof of Theorem 2.1 is complete. Setting p() we obtain the following corollary: Corollary 2.8 Let + a be analytic in D. Then 2 f () + f () <γπ 2 <γπ 2. Theorem 2.7 Let p() 1 + a 1 + be analytic in D with p() 1 and let γ (0, 1]. Then ] 2 p() + p () p() 2 + p () p 2 () <γ π 2 p() <γπ 2. Proof We only need to show that p q, where q is given by (2.6). As in the proof of Theorem 2.6, there exist a point 0 D such that the equalities (2.7) and (2.8) holds. We have
10 1252 S. Kanas, A.-E. Tudor 2 p + 0 p ] p p p p p + 2 p p p 2 2x 2γ + u 2 + 3ux γ sin γ π (xi)γ 2 + 4x 2γ cos 2 γ π 2 + (u + 2xγ sin γ π 2 ) ux γ cos γ π ] 2 +i 4x 2γ cos 2 γ π 2 + (u + 2xγ sin γ π 2 ), ( x 2 ) + 1 where u mγ > 0. 2x We notice that for γ (0, 1] the trigonometric functions sin and cos are located in the first quadrant of trigonometric circle and, therefore, have positive values. It follows that 2 p + 0 p ] p p γ π 2 + arctan u cos γ π 2 2x γ + u 2 x γ + 3u sin γ π γ π p 2 2 2, and this is contradiction with the hypothesis of the theorem. Thus, the proof is complete. Setting p() f () we obtain Corollary 2.9 Let + a be analytic in D. Then 2 f () ] 1 + f () f () 1 + f () + f () f () <γ π 2 f () <γπ 2. Acknowledgments This work was possible with the financial support of the Sectoral Operation Programme for Human esources Development , co-financed by the European Social Fund, under the project number POSDU/107/1.5/S/76841 with the title Modern Doctoral Studies: Internationaliation and Interdisciplinarity. This work was partially supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge, Faculty of Mathematics and Natural Sciences, University of esow. eferences 1. Ali.M., Nagpal S., avichandran, V.: Second-order differential subordination for analytic functions with fixed initial coefficient. Bull. Malays. Math. Sci. Soc. (2) 34(3), (2011)
11 Differential Subordinations and Harmonic Means Kanas S., Lecko A., Stankiewic J.: Differential subordinations and geometric means. Compl. Var. 44. Theor. Appl. 28, (1996) 3. Kanas S., Stankiewic J.: Arithmetic means with reference to convexity conditions, Bull. Soc. Sci. Lett. Łódź 47, Ser. ech. Deform. 24, (1997) 4. Kanas, S., Lecko, A.: Univalence criteria connected with arithmetic and geometric means, II. Folia Sci. Univ. Tech. esov. 20, (1996) 5. Kanas S., Lecko A.: Univalence criteria connected with arithmetic and geometric means, II. In: Proceedings of the Second International Workshop of Transform Methods and Special Functions, Varna 96, pp Bulgarian Academy of Sciences, Sofia (1996) 6. Kim, Y.Ch., Lecko, A.: On differential subordinations related to convex functions. J. Math. Anal. Appl. 235, (1999) 7. Lecko A., Lecko M.: Differential subordinations of arithmetic and geometric means of some functionals related to a sector. Int. J. Math. Math. Sci. 2011, Article ID , 19 (2011) 8. Lewandowski, Z., Miller, S.S., Złotkiewic, E.: Generating functions for some classes of univalent functions. Proc. Am. Math. Soc. 56, (1976) 9. Liu J.-L.: Certain sufficient conditions for strongly starlike functions associated with an integral operator. Bull. Malays. Math. Sci. Soc. (2) 34(1), (2011) 10. Miller, S.S., Mocanu, P.T.: Differential Subordinations: Theory and Applications. Dekker, New York (2000) 11. Mocanu, P.T.: Une propriété de convexité dans la théorie de représentation conforme. Stud. Univ. Babes-Bolyai 34(11), (1969) 12. Mondal S.., Swaminathan A.: Geometric properties of generalied Bessel functions. Bull. Malays. Math. Sci. Soc. (2) 35(1), (2012) 13. Omar,., Halim S.A.: Multivalent harmonic functions defined by Diok-Srivastava operator. Bull. Malays. Math. Sci. Soc. (2) 35(3), (2012) 14. ăducanu, D., Nechita, V.O.: On α- convex analytic functions defined by generalied uscheweyh operator. Stud. Univ. Babeş-Bolyai 53, (2008) 15. uscheweyh, S.: New criteria for univalent functions. Proc. Am. Math. Soc. 49, (1975) 16. Ali,.M., avichandran, V.: Classes of meromorphic α- convex functions. Taiwan. J. Math. 14, (2010) 17. Supramaniam, S., Ali.M., Lee S.K., avichandran, V.: Convolution and differential subordination for multivalent functions. Bull. Malays. Math. Sci. Soc. (2) 32(3), (2009) 18. Sălăgean, G.: Subclasses of Univalent Functions, Lecture Notes in Math, vol Springer, Berlin (1983)
A 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationOn Starlike and Convex Functions with Respect to 2k-Symmetric Conjugate Points
Tamsui Oxford Journal of Mathematical Sciences 24(3) (28) 277-287 Aletheia University On Starlike and Convex Functions with espect to 2k-Symmetric Conjugate Points Zhi-Gang Wang and Chun-Yi Gao College
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 informationarxiv: v1 [math.cv] 7 Jul 2016
UNIVALENCE AND QUASICONFORMAL EXTENSION OF AN INTEGRAL OPERATOR ERHAN DENIZ, STANIS LAWA KANAS, AND HALIT ORHAN arxiv:167.298v1 [math.cv] 7 Jul 216 Abstract. In this paper we give some sufficient conditions
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 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 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 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 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 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 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 informationOn the Class of Functions Starlike with Respect to a Boundary Point
Journal of Mathematical Analysis and Applications 261, 649 664 (2001) doi:10.1006/jmaa.2001.7564, available online at http://www.idealibrary.com on On the Class of Functions Starlike with Respect to a
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 informationSOME RESULTS ASSOCIATED WITH FRACTIONAL CALCULUS OPERATORS INVOLVING APPELL HYPERGEOMETRIC FUNCTION
Volume 29), Issue, Article 4, 7 pp. SOME RESULTS ASSOCIATED WITH FRACTIONAL CALCULUS OPERATORS INVOLVING APPELL HYPERGEOMETRIC FUNCTION R. K. RAINA / GANPATI VIHAR, OPPOSITE SECTOR 5 UDAIPUR 332, RAJASTHAN,
More informationA NOTE ON RUSCHEWEYH TYPE OF INTEGRAL OPERATORS
IJMMS 29:3 2002 183 186 PII S0161171202006920 http://ijmmshindawicom Hindawi Publishing Corp A NOTE ON RUSCHEWEYH TYPE OF INTEGRAL OPERATORS FOR UNIFORMLY -CONVEX FUNCTIONS M ANBU DURAI and R PARVATHAM
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 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 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 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 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 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 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 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 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 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 A New Class of Meromorphic Functions Associated with Spirallike Functions
Applied Mathematics Volume 202, Article ID 49497, 2 pages doi:0.55/202/49497 Research Article A New Class of Meromorphic Functions Associated with Spirallike Functions Lei Shi, Zhi-Gang Wang, and Jing-Ping
More informationOn the Iyengar Madhava Rao Nanjundiah inequality and its hyperbolic version
Notes on Number Theory and Discrete Mathematics Print ISSN 110 51, Online ISSN 67 875 Vol. 4, 018, No., 14 19 DOI: 10.7546/nntdm.018.4..14-19 On the Iyengar Madhava Rao Nanjundiah inequality and its hyperbolic
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 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 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 informationGrowth and distortion theorem for the Janowski alpha-spirallike functions in the unit disc
Stud. Univ. Babeş-Bolyai Math. 57(01), No., 55 59 Growth and distortion theorem for the Janowski alpha-spirallike functions in the unit disc Yaşar Polato glu Abstract. Let A be the class of all 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 informationAn ordinary differentail operator and its applications to certain classes of multivalently meromorphic functions
Bulletin of Mathematical analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 1, Issue 2, (2009), Pages 17-22 An ordinary differentail operator and its applications to certain
More informationCoefficient Estimates and Bloch s Constant in Some Classes of Harmonic Mappings
Bull. Malays. Math. Sci. Soc. (06) 39:74 750 DOI 0.007/s40840-05-038-9 Coefficient Estimates and Bloch s Constant in Some Classes of Harmonic Mappings S. Kanas D. Klimek-Smȩt Received: 5 September 03 /
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 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 informationCoefficient Bounds for a Certain Class of Analytic and Bi-Univalent Functions
Filomat 9:8 (015), 1839 1845 DOI 10.98/FIL1508839S Published by Faculty of Sciences Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Coefficient Bounds for a Certain
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 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 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 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 informationA Certain Subclass of Multivalent Functions Involving Higher-Order Derivatives
Filomat 30:1 (2016), 113 124 DOI 10.2298/FIL1601113S Published by Faculty of Sciences Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat A Certain Subclass of Multivalent
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 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 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 informationarxiv: v2 [math.cv] 24 Nov 2017
adii of the β uniformly convex of order α of Lommel and Struve functions Sercan Topkaya, Erhan Deniz and Murat Çağlar arxiv:70.0975v [math.cv] 4 Nov 07 Department of Mathematics, Faculty of Science and
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 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 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 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 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 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 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 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 informationFaber polynomial coefficient bounds for a subclass of bi-univalent functions
Stud. Univ. Babeş-Bolyai Math. 6(06), No., 37 Faber polynomial coefficient bounds for a subclass of bi-univalent functions Şahsene Altınkaya Sibel Yalçın Abstract. In this ork, considering a general subclass
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 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 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 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 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 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 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 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 informationHARMONIC CLOSE-TO-CONVEX MAPPINGS
Applied Mathematics Stochastic Analysis, 15:1 (2002, 23-28. HARMONIC CLOSE-TO-CONVEX MAPPINGS JAY M. JAHANGIRI 1 Kent State University Department of Mathematics Burton, OH 44021-9500 USA E-mail: jay@geauga.kent.edu
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 informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics INTEGRAL MEANS INEQUALITIES FOR FRACTIONAL DERIVATIVES OF SOME GENERAL SUBCLASSES OF ANALYTIC FUNCTIONS TADAYUKI SEKINE, KAZUYUKI TSURUMI, SHIGEYOSHI
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 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 informationESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF CERTAIN SUBCLASSES OF BI-UNIVALENT FUNCTIONS
Miskolc Matheatical Notes HU e-issn 787-43 Vol. 7 (07), No., pp. 739 748 DOI: 0.854/MMN.07.565 ESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF CERTAIN SUBCLASSES OF BI-UNIVALENT FUNCTIONS BADR S. ALKAHTANI,
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 informationPerov s fixed point theorem for multivalued mappings in generalized Kasahara spaces
Stud. Univ. Babeş-Bolyai Math. 56(2011), No. 3, 19 28 Perov s fixed point theorem for multivalued mappings in generalized Kasahara spaces Alexandru-Darius Filip Abstract. In this paper we give some corresponding
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 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 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 informationMajorization for Certain Classes of Meromorphic Functions Defined by Integral Operator
Int. J. Open Problems Complex Analysis, Vol. 5, No. 3, November, 2013 ISSN 2074-2827; Copyright c ICSRS Publication, 2013 www.i-csrs.org Majorization for Certain Classes of Meromorphic Functions Defined
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 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 informationOn products of multivalent close-to-star functions
Arif et al. Journal of Inequalities and Alications 2015, 2015:5 R E S E A R C H Oen Access On roducts of multivalent close-to-star functions Muhammad Arif 1,JacekDiok 2*,MohsanRaa 3 and Janus Sokół 4 *
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 information