ON THE FEKETE-SZEGÖ INEQUALITY FOR A CLASS OF ANALYTIC FUNCTIONS DEFINED BY USING GENERALIZED DIFFERENTIAL OPERATOR
|
|
- Denis Lester
- 5 years ago
- Views:
Transcription
1 Acta Universitatis Apulensis ISSN: No. 6/0 pp ON THE FEKETE-SZEGÖ INEQUALITY FOR A CLASS OF ANALYTIC FUNCTIONS DEFINED BY USING GENERALIZED DIFFERENTIAL OPERATOR Salma Faraj Ramadan, Maslina Darus Abstract. In this present investigation, the Fekete- Szegö inequality for certain normalized analytic functions f defined on the open unit disk for which zdk α,β,λ,δ fz)) Dα,β,λ,δ k fz) k N 0, α, β, λ, δ 0) lies in a region starlike with respect to and is symmetric with respect to the real axis will be obtained. In addition, certain applications of the main result for a class of functions defined by convolution are given. As a special case of this result, Fekete- Szegö inequality for a class of functions defined by fractional derivative is obtained. The motivation of this paper is due to the work given by Srivastava and Mishra in Mathematics Subject Classification: 30C45. Key words: Analytic function, Starlike functions, Derivative operator, Fekete- Szegö inequality.. Introduction Let A be the class of functions f of the form f z) = z + a n z n ) which are analytic in the open unit disk U = {z : z C and z < }. Further, let S denote the class of functions which are univalent in U. For a function f A, we define D 0 f z) = f z) 67
2 D α,β,λ,δ f z) = λ δ) β α) f z) + λ δ) β α) zf z) = z + λ δ) β α) n ) + a n z n D k α,β,λ,δ f z) = D α,β,λ,δ. D k α,β,λ,δ f z) ) Dα,β,λ,δ k f z) = z + λ δ) β α) n ) + k a n z n ) for α 0, β 0, λ 0, δ 0, λ > δ, β > α) and k {0,,,...}. Remark. i) When α = 0, δ = 0, λ =, β =, it reduces to Sǎlǎgean differential operator9. ii) When α = 0, reduces to Darus and Ibrahim differential operator. iii) And when α = 0, δ = 0, β =, reduces to Al- Oboudi differential operator. Let φ z) be an analytic function with positive real part on U with φ z) =, φ z) > 0 which maps the unit disk U onto a region starlike with respect to which is symmetric with respect to the real axis. Let S φ) be the class of functions in f z) S for which zf z) φ z), z U) f z) and C φ) be the class of functions in f z) S for which + zf z) f z) φ z), z U) where denotes the subordination between analytic functions. These classes were investigated and studied by Ma and Minda 4. They have obtain the Fekete- Szegö inequality for the functions in the class C φ). Since f C φ) if and only if zf z) S φ), we get the Fekete- Szegö inequality for functions in the class S φ). For a brief history of the Fekete- Szegö problem for class of starlike, convex, and close to convex functions, see the recent paper by Srivastava et.al 7. In the present paper, we obtain the Fekete- Szegö inequality for the class Mα,β,λ,δ k φ) as defined below. Also we give applications of our result to certain functions defined through convolution or Hadamard product) and in particular we consider a class Mα,β,λ,δ k φ) 68
3 defined by fractional derivatives. The object of this paper is to generalize the Fekete- Szegö inequality of that given by Srivastava and Mishra 6. Definition. Let φ z) be a univalent starlike function with respect to which maps the unit disk U onto a region in the right half plane which is symmetric with respect to the real axis, φ 0) = and φ 0) > 0. A function f A is in the class Mα,β,λ,δ k φ) if ) z Dα,β,λ,δ k f z) Dα,β,λ,δ k f z) φ z). For fixed g A, we define the class M k,g α,β,λ,δ φ) to be the class of functions f A for which f g) Mα,β,λ,δ k φ). In order to derive our main results, we have to recall here the following lemma 4: Lemma. If p z) = + c z + c z +... is an analytic function with positive real part in U, then c νc 4ν + if ν 0; if 0 ν ; 4ν if ν. When ν < 0 or ν >, the equality holds if and only if p z) is + z)/ z) or one of its rotations. If 0 < ν <, then the equality holds if and only if p z) is + z )/ z ) or one of its rotations. If ν = 0, the equality holds if and only if ) + γ + z p z) = z + γ ) z, 0 γ ) + z or one of its rotations. If ν =, the equality holds if and only if p z) is the reciprocal of one of the functions such that the equality holds in the case of ν = 0. Also the above upper bound is sharp, and it can be improved as follows when 0 < ν < : c νc + ν c 0 < ν ) and c νc + ν) c ) < ν..fekete-szegö problem Our main result is the following: Theorem. Let φ z) = + B z + B z +... If f z) given by ) belongs to 69
4 M k α,β,λ,δ φ), then a3 µa B λ δ)β α)+ k µb λ δ)β α)+ k + B λ δ)β α)+ k if µ σ ; B λ δ)β α)+ k ifσ µ σ ; 3) B + λ δ)β α)+ k µb λ δ)β α)+ k B λ δ)β α)+ k if µ σ, where The result is sharp. Proof. For f Mα,β,λ,δ k φ), let σ := λ δ) β α) + { k B B ) + B } λ δ) β α) + k B σ := λ δ) β α) + { k B + B ) + B } λ δ) β α) + k. B p z) = ) z Dα,β,λ,δ k f z) D k α,β,λ,δ f z) = + b z + b z ) From 4), we obtain λ δ) β α) + k a = b, λ δ) β α) + k a 3 = λ δ) β α) + k a + b. 5) Since φ z) is univalent and p φ, the function is analytic and positive real in U. Also we have p z) = + φ p z)) φ p z)) = + c z + c z +... p z) = φ ) p z), 6) p z) + 70
5 ) and from this equality and 4), + b z + b z +... = φ c z+c z c z+c z +... = φ c z + c ) c z +... ) = +B c z+b c ) c z +...+B... we obtain b = B c and b = B c ) c + Where ν = a 3 µa = B 4 λ δ) β α) + k c c 4 c z + 4 B c. Therefore, we have { B B )} λ δ) β α) + k µ λ δ) β α) + k λ δ) β α) + k B, B B a 3 µa = B { c 4 λ δ) β α) + k νc }. ) λ δ) β α) + k µ λ δ) β α) + k λ δ) β α) + k B. If µ σ, then by applying Lemma, we get a 3 µa B λ δ) β α) + k µb λ δ) β α) + k + B λ δ) β α) + k which is the first part of assertion 3). Next, if µ σ, by applying Lemma, we get a 3 µa B λ δ) β α) + k + µb λ δ) β α) + k B λ δ) β α) + k. if µ = σ, then equality holds if and only if ) ) + γ + z γ z p z) = z +, 0 γ, z U) + z or one of its rotations. if µ = σ, then B B ) λ δ) β α) + k µ λ δ) β α) + k λ δ) β α) + k B = 0. Therefore, p z) = + γ ) + z z + γ 7 ) z, 0 < γ <, z U). + z
6 Finally, we see that and a 3 µa = B 4 λ δ) β α) + k c c { B B } λ δ) β α) + k µ λ δ) β α) + k λ δ) β α) + k B max B B ) λ δ) β α) + k µ λ δ) β α) + k λ δ) β α) + k B, Therefore using Lemma, we get σ µ σ ). a3 µa B c = 4 λ δ) β α) + k B λ δ) β α) + k, σ µ σ ). If σ < µ < σ, then we have z p z) = p z) = + νz, 0 ν ). νz Our result now follows by an application of Lemma. To show that the bounds are sharp, we define the function Ks φ s =, 3,...) by ) Dα,β,λ,δ k Kφ s z) D k α,β,λ,δ Kφ s z) = φ z s ), K φ s 0) = 0 = K φ s 0) and the function F γ and G γ, 0 γ ) by ) z Dα,β,λ,δ k F γ z) ) z z + ν) Dα,β,λ,δ k F = φ, F γ 0) = 0 = F γ 0) γ z) + νz and ) z Dα,β,λ,δ k G γ z) D k α,β,λ,δ G γ z) ) z z + ν) = φ + νz, G γ 0) = 0 = G γ 0). 7
7 Clearly the functions K φ s, F γ, G γ M k α,β,λ,δ φ). Also we write Kφ = K φ. If µ < σ or µ > σ, then the equality holds if and only if f is Ks φ or one of its rotations. When σ < µ < σ, the equality holds if and only if f is K φ 3 or one of its rotations. If µ = σ, then the equality holds if and only if f is F γ or one of its rotations. If µ = σ, then the equality holds if and only if f is G γ or one of its rotations. Remark. If σ µ σ, then in view of Lemma, Theorem can be improved. Let σ 3 be given by If σ µ σ 3, then If σ 3 µ σ, then σ 3 := λ δ) β α) + k B + B ) λ δ) β α) + k. B a3 µa λ δ) β α) + k + λ δ) β α) + k B µ λ δ) β α) + k λ δ) β α) + k B B + λ δ) β α) + k B B λ δ) β α) + k. a 3 µa λ δ) β α) + k + λ δ) β α) + k B B + B µ λ δ) β α) + k λ δ) β α) + k λ δ) β α) + k B B λ δ) β α) + k. Proof. For the values of σ µ σ 3, we have a 3 µa + µ σ ) a = a a B 4 λ δ) β α) + k c νc B + µ σ ) 4 λ δ) β α) + k c 73
8 = B 4 λ δ) β α) + k c νc + + µ λ δ) β α) { +k B B ) + B }) B λ δ) β α) + k B 4 λ δ) β α) + k c = = { B λ δ) β α) + k c νc + ν c } Similarly, for the value of σ 3 µ σ, we write a 3 µa + σ µ) a = B λ δ) β α) + k. + B 4 λ δ) β α) + k c νc B + σ µ) 4 λ δ) β α) + k c B = 4 λ δ) β α) + k c νc + λ δ) β α) + k { B + B ) + B } λ δ) β α) + k B µ ) B 4 λ δ) β α) + k c = = { B c λ δ) β α) + k νc + ν) c } Thus, Remark holds. B λ δ) β α) + k. 3. Applications to Functions Defined by Fractional Derivatives For two analytic functions f z) = z + a n z n and g z) = z + b n z n, their convolution or Hadamard product) is defined to be the function f g) z) given by f g) z) = f z) g z) = z + a n b n z n. 74
9 Definition.8 Let f be analytic in a simply-connected region of the z-plane containing the region. The fractional derivative of f of order γ is defined by Dz γ d f z) Γ γ) dz z 0 f ζ) z ζ) γ dζ, 0 γ < ), where the multiplicity of z ζ) γ is removed by requiring that log z ζ) is real for z ζ > 0. Using the above definition and its known extensions involving fractional derivatives and fractional integrals, Owa and Srivastava 5 introduced the operator Ω γ : A A defined by Ω γ f) z) = Γ γ) z γ D γ z f z), γ, 3, 4,...). The class M k,γ α,β,λ,δ φ) consists of functions f A for which Ωγ f Mα,β,λ,δ k φ). Note that M k,γ k,g α,β,λ,δ φ) is the special case of the class Mα,β,λ,δ φ) when Let Since g z) = z + g z) = z + Γ n + ) Γ γ) z n. 7) Γ n + γ) g n z n, g n > 0). Dα,β,λ,δ k f z) = z + λ δ) β α) n ) + k a n z n M g α,β,λ,δ φ) if and only if D k α,β,λ,δ f g ) z) = z + λ δ) β α) n ) + k a n g n z n Mα,β,λ,δ k φ) 8) we obtain the coefficient estimate for functions in the class M k,g α,β,λ,δ φ), from the corresponding estimate for functions in the class Mα,β,λ,δ k φ). Applying Theorem for the operator 8), we get the following Theorem after an obvious change of the parameter µ : Theorem. Let g z) = z + g k z k, g k > 0) and let the function φ z) be given by φ z) = + n= k= B n z n. If operator ) belongs to M k,g α,β,λ,δ φ), then 75
10 a 3 µa B g 3 λ δ)β α)+ k B g 3 λ δ)β α)+ k g 3 B + λ δ)β α)+ k µg 3 B λ δ)β α)+ k + µg 3 B λ δ)β α)+ k B λ δ)β α)+ k B λ δ)β α)+ k if µ σ ; ifσ µ σ ; if µ σ, where σ := g λ δ) β α) + { k B B ) + B } g 3 λ δ) β α) + k B σ := g λ δ) β α) + { k B + B ) + B } g 3 λ δ) β α) + k. B The result is sharp. Since Ω γ D k α,β,λ,δ f ) z) = z + we have and g 3 : g := Γ n + ) Γ γ) Γ n + γ) Γ 3) Γ γ) Γ 3 γ) Γ 4) Γ 3 γ) Γ 4 γ) = λ δ) β α) n ) + k a n z n = γ 9) 6 γ) 3 γ). 0) For g and g 3 given by 9) and 0), Theorem reduces to the following: Theorem 3. Let g z) = z + g k z k, by φ z) = + a 3 µa n= k= g k > 0) and let the function φ z) be given B n z n. If Dα,β,λ,δ k k,γ f given by ) belongs to Mα,β,λ,δ φ), then 76
11 γ)3 γ) 6 γ)3 γ) 6 γ)3 γ) 6 B λ δ)β α)+ k B λ δ)β α)+ k B + λ δ)β α)+ k 3 γ)µb 3 γ)λ δ)β α)+ k + 3 γ)µb 3 γ)λ δ)β α)+ k B if µ σ λ δ)β α)+ k ; B λ δ)β α)+ k ifσ µ σ ; if µ σ, where σ := 3 γ) λ δ) β α) + { k B B ) + B } 3 γ) λ δ) β α) + k B σ := 3 γ) λ δ) β α) + { k B + B ) + B } 3 γ) λ δ) β α) + k. B The result is sharp. Remark 3. When k = 0, λ =, β =, α = 0, δ = 0, B = 8 and B π = 6 the above Theorem 3 reduces to a recent result of Srivastava and Mishra 6, 3π Theorem 8, P.64) for a class of functions for which Ω γ f z) is a parabolic starlike functions see 3,5). Note also, other work related to the upper bounds of the Fekete-Szegó theorem can be found in 0. Acknowledgement: The work here is fully supported by UKM-ST-06-FRGS References F. M. Al-Oboudi, On univalent functions defined by a generalized Sǎlǎgean operator, Int. J. Math. Math. Sci., 7 004), M. Darus and R. W. Ibrahim, On subclasses for generalized operators of complex order, Far East Journal of Math. Sci.FJMS), 333) 009), B. Frasin, and M. Darus, On Fekete- Szegö problem using Hadamard products, Intern. Math. Jour., 3 003), W. Ma and D. Minda, A unified treatment of some speial classes of univalent functions, in: Proceeding of the conference on complex analysis, Z. Li. F. Ren, L. Yang, and S. Zhang Eds.), Int. Press 994), S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad J. Math., 39 5) 987),
12 6 H. M. Srivastava and A. K. Mishra, Applications of fractional calculus to parabolic starlike and uniformly convex functions, Comput. Math. Appl., ), H. M. Srivastava, A. K. Mishra and M. K. Das, The Fekete- Szegö problem for a subclass of close-to-convex functions, Complex Variables Theory Appl., 44 00), H. M. Srivastava and S. Owa, Univalent functions, fractional calculus and their applications., John Wiley and Sons, New Jersey, 989). 9 G. S. Sǎlǎgean, Subclasses of univalent functions, Lecture Notes in Math.03, Springer, Verlag Berlin, 983), PP S. P. Goyal and Pranay Goswami, Certain coefficient inequalities for Sakaguchi type functions and applications to fractional derivative operator, Acta Universitatis Apulensis, No. 9/009, Salma Faraj Ramadan School of Mathematical Sciences Faculty of Science and Technology Universiti Kebangsaan Malaysia salma.naji@gmail.com Maslina Darus School of Mathematical Sciences Faculty of Science and Technology Universiti Kebangsaan Malaysia maslina@ukm.my 78
Coefficient 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 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 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 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 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 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 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 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 informationA NOTE ON A SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY A GENERALIZED SĂLĂGEAN OPERATOR. Alina Alb Lupaş, Adriana Cătaş
Acta Universitatis Apulensis ISSN: 158-539 No. /010 pp. 35-39 A NOTE ON A SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY A GENERALIZED SĂLĂGEAN OPERATOR Alina Alb Lupaş, Adriana Cătaş Abstract. By means of
More 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationOn Some α-convex Functions
Int. J. Open Problems Comput. Sci. Math., Vol. 1, No. 1, June 2008 On Some α-convex Functions Mugur Acu 1, Fatima Al-Oboudi 2, Maslina Darus 3, Shigeyoshi Owa 4 Yaşar Polato glu 5 and Emel Yavuz 5 1 Department
More informationCERTAIN DIFFERENTIAL SUPERORDINATIONS USING A GENERALIZED SĂLĂGEAN AND RUSCHEWEYH OPERATORS. Alb Lupaş Alina
Acta Universitatis Apulensis ISSN: 1582-5329 No. 25/211 pp. 31-4 CERTAIN DIFFERENTIAL SUPERORDINATIONS USING A GENERALIZED SĂLĂGEAN AND RUSCHEWEYH OPERATORS Alb Lupaş Alina Abstract. In the present paper
More 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 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 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 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 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 informationA NOVEL SUBCLASS OF UNIVALENT FUNCTIONS INVOLVING OPERATORS OF FRACTIONAL CALCULUS P.N. Kamble 1, M.G. Shrigan 2, H.M.
International Journal of Applied Mathematics Volume 30 No. 6 2017, 501-514 ISSN: 1311-1728 printed version; ISSN: 1314-8060 on-line version doi: http://dx.doi.org/10.12732/ijam.v30i6.4 A NOVEL SUBCLASS
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 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 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 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 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 informationA NOTE ON UNIVALENT FUNCTIONS WITH FINITELY MANY COEFFICIENTS. Abstract
A NOTE ON UNIVALENT FUNCTIONS WITH FINITELY MANY COEFFICIENTS M. Darus, R.W. Ibrahim Abstract The main object of this article is to introduce sufficient conditions of univalency for a class of analytic
More informationDIFFERENTIAL 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 informationFUNCTIONS WITH NEGATIVE COEFFICIENTS
A NEW SUBCLASS OF k-uniformly CONVEX FUNCTIONS WITH NEGATIVE COEFFICIENTS H. M. SRIVASTAVA T. N. SHANMUGAM Department of Mathematics and Statistics University of Victoria British Columbia 1V8W 3P4, Canada
More informationThe Fekete-Szegö Theorem for a Certain Class of Analytic Functions (Teorem Fekete-Szegö Bagi Suatu Kelas Fungsi Analisis)
Sains Malaysiana 40(4)(2011): 385 389 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*
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 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 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 ESTIMATE FOR SECOND AND THIRD COEFFICIENTS FOR A NEW SUBCLASS OF ANALYTIC AND BI-UNIVALENT FUNCTIONS BY USING DIFFERENTIAL OPERATORS
Palestine Journal of Mathematics Vol. 8(1)(019), 44 51 Palestine Polytechnic University-PPU 019 ON ESTIMATE FOR SECOND AND THIRD COEFFICIENTS FOR A NEW SUBCLASS OF ANALYTIC AND BI-UNIVALENT FUNCTIONS BY
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 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 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 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 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 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 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 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 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 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 INCLUSION PROPERTIES OF STARLIKE AND CONVEX FUNCTIONS ASSOCIATED WITH HOHLOV OPERATOR. II
italian journal of pure and applied mathematics n. 37 2017 117 126 117 SOME INCLUSION PROPERTIES OF STARLIKE AND CONVEX FUNCTIONS ASSOCIATED WITH HOHLOV OPERATOR. II M. Kasthuri K. Vijaya 1 K. Uma School
More 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 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 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 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 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 informationOn a New Subclass of Salagean Type Analytic Functions
Int. Journal of Math. Analysis, Vol. 3, 2009, no. 14, 689-700 On a New Subclass of Salagean Type Analytic Functions K. K. Dixit a, V. Kumar b, A. L. Pathak c and P. Dixit b a Department of Mathematics,
More 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 informationTwo Points-Distortion Theorems for Multivalued Starlike Functions
Int. Journal of Math. Analysis, Vol. 2, 2008, no. 17, 799-806 Two Points-Distortion Theorems for Multivalued Starlike Functions Yaşar Polato glu Department of Mathematics and Computer Science TC İstanbul
More 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 On Generalisation of Polynomials in Complex Plane
Hindawi Publishing Corporation Advances in Decision Sciences Volume 21, Article ID 23184, 9 pages doi:1.1155/21/23184 Research Article On Generalisation of Polynomials in Complex Plane Maslina Darus and
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 informationApplied 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 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 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 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 informationResearch Article Coefficient Estimates for Two New Subclasses of Biunivalent Functions with respect to Symmetric Points
Function Spaces Volume 2015 Article ID 145242 5 pages http://dx.doi.org/10.1155/2015/145242 Research Article Coefficient Estimates for Two New Subclasses of Biunivalent Functions with respect to Symmetric
More informationOn neighborhoods of functions associated with conic domains
DOI: 0.55/auom-205-0020 An. Şt. Univ. Ovidius Constanţa Vol. 23(),205, 29 30 On neighborhoods of functions associated with conic domains Nihat Yağmur Abstract Let k ST [A, B], k 0, B < A be the class of
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 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 informationCOEFFICIENT ESTIMATES FOR A SUBCLASS OF ANALYTIC BI-UNIVALENT FUNCTIONS
Bull. Korean Math. Soc. 0 (0), No. 0, pp. 1 0 https://doi.org/10.4134/bkms.b170051 pissn: 1015-8634 / eissn: 2234-3016 COEFFICIENT ESTIMATES FOR A SUBCLASS OF ANALYTIC BI-UNIVALENT FUNCTIONS Ebrahim Analouei
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 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 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 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 informationBulletin of the Transilvania University of Braşov Vol 8(57), No Series III: Mathematics, Informatics, Physics, 1-12
Bulletin of the Transilvania University of Braşov Vol 857), No. 2-2015 Series III: Mathematics, Informatics, Physics, 1-12 DISTORTION BOUNDS FOR A NEW SUBCLASS OF ANALYTIC FUNCTIONS AND THEIR PARTIAL SUMS
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 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 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 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 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 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 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 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 informationCoefficient Inequalities for Classes of Uniformly. Starlike and Convex Functions Defined by Generalized. Ruscheweyh Operator
International Mathematical Forum, Vol. 6, 2011, no. 65, 3227-3234 Coefficient Inequalities for Classes of Uniformly Starlike Convex Functions Defined by Generalized Ruscheweyh Operator Hesam Mahzoon Department
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 information