Univalent and Starlike Generalized Hypergeometric Functions

Owa, Shigeyoshi; Srivástava, H. M.

doi:10.4153/cjm-1987-054-3

Cited by 286 publications

(145 citation statements)

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“…is the fractional derivative of f of order γ ; 2,3, 4,.. γ ≠ , [6] . Also, note that the operators J(0,0, 2, n 1)f (z); + n ∈ N due to Noor [7,8] ) and J(0,0, b,a)f (z); a > 0, b > 0 due to Choi al et.…”

Section: Methodsmentioning

confidence: 99%

On New Bijective Convolution Operator Acting for Analytic Functions

Al-Refai¹,

Darus²

2009

J. of Mathematics and Statistics

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Problem statement:We introduced a new bijective convolution linear operator defined on the class of normalized analytic functions. This operator was motivated by many researchers namely Srivastava, Owa, Ruscheweyh and many others. The operator was essential to obtain new classes of analytic functions. Approach: Simple technique of Ruscheweyh was used in our preliminary approach to create new bijective convolution linear operator. The preliminary concept of Hadamard products was mentioned and the concept of subordination was given to give sharp proofs for certain sufficient conditions of the linear operator aforementioned. In fact, the subordinating factor sequence was used to derive different types of subordination results. Results: Having the linear operator, subordination theorems were established by using standard concept of subordination. The results reduced to wellknown results studied by various researchers. Coefficient bounds and inclusion properties, growth and closure theorems for some subclasses were also obtained. Conclusion: Therefore, many interesting results could be obtained and some applications could be gathered.

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Section: Methodsmentioning

confidence: 99%

On New Bijective Convolution Operator Acting for Analytic Functions

Al-Refai¹,

Darus²

2009

J. of Mathematics and Statistics

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“…. , then L(a, c) has an inverse L(c, a) and is a one-one mapping of A onto itself (see Owa and Srivastava [26]). …”

Section: Application Of the Convolution On Certain Integral Operatormentioning

confidence: 99%

Some properties of generalized convolution of harmonic univalent functions

Porwal

Dixit

2013

Demonstratio Mathematica

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Abstract. The purpose of the present paper is to investigate some interesting properties on generalized convolutions of functions for the classes HP * (α), HS(α) and HC(α). Further, an application of the convolution on certain integral operator are mentioned. IntroductionA continuous complex-valued function f = u + iv defined in a simply connected complex domain D is said to be harmonic in D, if both u and v are real harmonic in D. In any simply connected domain we can write f = h+g, where h and g are analytic in D. We call h the analytic part and g the coanalytic part of f. A necessary and sufficient condition for f to be locally univalent and sense-preserving in D is that |h ′ (z)| > |g ′ (z)|, z ∈ D, (see ). For more basic results on harmonic functions one may refer following standard introductory text book by Duren [14], (see also Ahuja [1] and Ponnusamy and Rasila [28,29]Denote by S H the class of functions f = h+g that are harmonic univalent and sense-preserving in the unit disc U = {z : |z| < 1} for which f (0) = f z (0) − 1 = 0. Then, for f = h + g ∈ S H , we may express the analytic functions h and g asA function f (z) of the form (1.1) in S H is said to be harmonic starlike of order α, (0 ≤ α < 1) in U , if and only if (1.2) ∂ ∂θ {arg f (z)} > α, z ∈ U,2000 Mathematics Subject Classification: 30C45, 26D15.

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“…where [5]), includes (as its special cases) various other linear operators introduced and studied by Carlson and Shaffer [3], Ruscheweyh [10] and OwaSrivastava [9]. Motivated by earlier works of Aouf et al, [1] and Dziok and Raina [6] we define the following new subclass of T involving hypergeometric functions.…”

Section: Introductionmentioning

confidence: 99%