Starlike and Prestarlike Hypergeometric Functions

Carlson, B. C.; Shaffer, Dorothy Browne

doi:10.1137/0515057

Cited by 368 publications

(173 citation statements)

References 15 publications

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“…w j z j where w j :¼ # b;s;c ðjÞa j and the function # b;s;c is defined in inequality (18), satisfied the following condition in class S as follows:…”

Section: Criteria For Hadamard Productmentioning

confidence: 99%

Upper bound of fractional differential operator related to univalent functions

2016

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In this article, we defined the generalized fractional differential Tremblay operator in the open unit disk that by usage the definition of the generalized SrivastavaOwa operator. In particular, we established a new operator denoted by H b;s;c z based on the normalized generalized fractional differential operator and represented by convolution product. Moreover, we studied the coefficient criteria of univalence, starlikeness and convexity for the last operator mentioned.

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“…w j z j where w j :¼ # b;s;c ðjÞa j and the function # b;s;c is defined in inequality (18), satisfied the following condition in class S as follows:…”

Section: Criteria For Hadamard Productmentioning

confidence: 99%

Upper bound of fractional differential operator related to univalent functions

2016

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“…Carlson and Shaffer [5] defined a linear operator L (a, c), corresponding to the function φ(a, c; z) on A via the convolution, where A is the class of functions of the form (3.1), which are analytic in the open unit disc U .…”

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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“…The hypergeometric function (1) plays an important role in the theory of univalent functions. Among the others de Branges [2], Carlson and Shaffer [3], Ruscheweyh and Singh [11], Lewis [7], Ponnusamy and Vuorinen [10] investigated it in various aspects. Now, we define the function $(a, c; z) by Many authors considered the classes of regular functions defined by subordination.…”

Section: \U(z) | < 1 (Zeu)mentioning

confidence: 99%

Univalence of Certain Analytic Functions

Trojnar-Spelina¹

1998

Demonstratio Mathematica

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Starlike and Prestarlike Hypergeometric Functions

Cited by 368 publications

References 15 publications

Upper bound of fractional differential operator related to univalent functions

Upper bound of fractional differential operator related to univalent functions

Some properties of generalized convolution of harmonic univalent functions

Univalence of Certain Analytic Functions

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