A subclass of harmonic univalent functions with negative coefficients

Karpuzogullari, Sibel Yalçin; Öztürk, Murat; Yamankaradeniz, Mümin

doi:10.1016/s0096-3003(02)00314-4

Cited by 14 publications

(15 citation statements)

References 4 publications

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“…If we put n = 2, c = 0 and α = 1 in Theorem 2.1, then we obtain the following result of Karpuzogullari et al [6].…”

Section: Resultsmentioning

confidence: 55%

“…Proof. Let f α be of the form (6) belonging to T H α n (β) for 0 ≤ β < 1. The mth quasi-partial sums F m (z) α of the integral operator F (z) α for functions f of the form (6) are as follows…”

Section: Resultsmentioning

confidence: 99%

“…iii For α = 1, n = 1, the class T H α n (β) reduces to HP (β) studied by Karpuzogullari et al in [6], (see also [2]).…”

Section: Introductionmentioning

confidence: 93%

“…The class HP (β) was introduced and extensively studied by Karpuzogullari et al [6]. Very recently, some other interesting properties such as generalized convolution and partial sums for this class HP (β) have been studied by Porwal and Dixit in [8] and [9], respectively.…”

Section: Introductionmentioning

confidence: 99%

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Quasi Partial Sums of Harmonic Univalent Functions

Aldweby

Darus

2019

rev.colomb.mat

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In this work, we obtain some conditions under which the quasi partial sums of the generalized Bernardi integral operator consisting of the harmonic univalent functions belongs to a similar class.Key words and phrases. quasi-partial sums, integral operator, harmonic functions.2010 Mathematics Subject Classification. 30C45, 30C50.Resumen. En este trabajo obtenemos algunas condiciones bajo las cuales las sumas cuasi-parciales del operador integral Bernardi generalizado que consiste de funciones armónicas univalentes pertenece a una clase similar.Palabras y frases clave. Sumas cuasi-parciales, operador integral, funciones armónicas.

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“…If we put n = 2, c = 0 and α = 1 in Theorem 2.1, then we obtain the following result of Karpuzogullari et al [6].…”

Section: Resultsmentioning

confidence: 55%

Section: Resultsmentioning

confidence: 99%

“…iii For α = 1, n = 1, the class T H α n (β) reduces to HP (β) studied by Karpuzogullari et al in [6], (see also [2]).…”

Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quasi Partial Sums of Harmonic Univalent Functions

Aldweby

Darus

2019

rev.colomb.mat

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“…In order to prove our results for functions to the class HP * (α), we shall need the following lemma given by Karpuzoǧullari et al [19]. …”

Section: Resultsmentioning

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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Harmonic Function with Correlated Coefficients

Dziok

2019

Acta Math Sci

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A subclass of harmonic univalent functions with negative coefficients

Cited by 14 publications

References 4 publications

Quasi Partial Sums of Harmonic Univalent Functions

Quasi Partial Sums of Harmonic Univalent Functions

Some properties of generalized convolution of harmonic univalent functions

Harmonic Function with Correlated Coefficients

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