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Title: On the order of convolution consistence of the analytic functions with negative coefficients (English)
Author: Sălăgean, Grigore S.
Author: Venter, Adela
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 142
Issue: 4
Year: 2017
Pages: 381-386
Summary lang: English
Category: math
Summary: Making use of a modified Hadamard product, or convolution, of analytic functions with negative coefficients, combined with an integral operator, we study when a given analytic function is in a given class. Following an idea of U. Bednarz and J. Sokół, we define the order of convolution consistence of three classes of functions and determine a given analytic function for certain classes of analytic functions with negative coefficients. (English)
Keyword: analytic function with negative coefficients
Keyword: univalent function
Keyword: extreme point
Keyword: order of convolution consistence
Keyword: starlikeness
Keyword: convexity
MSC: 30C45
MSC: 30C50
idZBL: Zbl 06819592
idMR: MR3739024
DOI: 10.21136/MB.2017.0019-15
Date available: 2017-11-20T15:02:26Z
Last updated: 2020-07-01
Stable URL:
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Reference: [5] Sălăgean, G. S.: Classes of univalent functions with two fixed points.Itinerant Seminar on Functional Equations, Approximation and Convexity, Cluj-Napoca, 1984 Univ. "Babeş-Bolyai'' (1984), 181-184. MR 0788744
Reference: [6] Sălăgean, G. S.: On univalent functions with negative coefficients.Prepr., "Babeş-Bolyai'' Univ., Fac. Math. Phys., Res. Semin. 7 (1991), 47-54. Zbl 0766.30010, MR 1206741
Reference: [7] Schild, A., Silverman, H.: Convolutions of univalent functions with negative coefficients.Ann. Univ. Mariae Curie-Skłodowska, Sect. A (1975) 29 (1977), 99-107. Zbl 0363.30018, MR 0457698
Reference: [8] Silverman, H.: Univalent functions with negative coefficients.Proc. Am. Math. Soc. 51 (1975), 109-116. Zbl 311.30007, MR 0369678, 10.2307/2039855


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