Mathematica Bohemica, online first, 6 pp.

On the order of convolution consistence of the analytic functions with negative coefficients

Grigore S. Sălăgean, Adela Venter

Received May 4, 2015.  First published February 2, 2017.

Abstract:  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.
Keywords:  analytic function with negative coefficients; univalent function; extreme point; order of convolution consistence; starlikeness; convexity
Classification MSC:  30C45, 30C50
DOI:  10.21136/MB.2017.0019-15

PDF available at:  Myris Trade   Institute of Mathematics CAS

[1] C. M. Balaeţi: An integral operator associated with differential superordinations. An. Ştiinţ. Univ. "Ovidius" Constanţa Ser. Mat. 17 (2009), 37-44. MR 2573368 | Zbl 1199.30049
  [2] U. Bednarz, J. Sokół: On order convolution consistence of the analytic functions. Stud. Univ. Babeş-Bolyai Math. 55 (2010), 45-51. MR 2764250 | Zbl 1240.30037
  [3] V. P. Gupta, P. K. Jain: Certain classes of univalent functions with negative coefficients. Bull. Aust. Math. Soc. 14 (1976), 409-416. DOI 10.1017/S0004972700025326 | MR 0414849 | Zbl 323.30016
  [4] G. S. Salagean: Subclasses of univalent functions. Complex Analysis, Proceedings 5th Rom.-Finn. Semin., Bucharest 1981, Part 1 (C. Andreian Cazacu at al., eds.) Lecture Notes in Math. 1013. Springer, Berlin (1983), 362-372. DOI 10.1007/BFb0066543 | MR 0738107 | Zbl 0531.30009
  [5] G. S. Salagean: 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
  [6] G. S. Sălăgean: On univalent functions with negative coefficients. Prepr., "Babeş-Bolyai" Univ., Fac. Math. Phys., Res. Semin. 7 (1991), 47-54. MR 1206741 | Zbl 0766.30010
  [7] A. Schild, H. Silverman: Convolutions of univalent functions with negative coefficients. Ann. Univ. Mariae Curie-Skłodowska, Sect. A (1975) 29 (1977), 99-107. MR 0457698 | Zbl 0363.30018
  [8] H. Silverman: Univalent functions with negative coefficients. Proc. Am. Math. Soc. 51 (1975), 109-116. DOI 10.2307/2039855 | MR 0369678 | Zbl 311.30007

Affiliations:   Grigore S. Sălăgean, Babes-Bolyai University, Faculty of Mathematics and Computer Science, Str. Kogalniceanu Nr. 1, 400084 Cluj-Napoca, Romania, e-mail:; Adela Venter, Faculty of Enviromental Protection, University of Oradea, Str. Universitatii Nr. 1, 410087 Oradea, Romania, e-mail:

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