| 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:
|
http://hdl.handle.net/10338.dmlcz/146977 |
| . |
| Reference:
|
[1] Bălăeţi, C. M.: An integral operator associated with differential superordinations.An. Ştiinţ. Univ. "Ovidius" Constanţa Ser. Mat. 17 (2009), 37-44. Zbl 1199.30049, MR 2573368 |
| Reference:
|
[2] Bednarz, U., Sokół, J.: On order convolution consistence of the analytic functions.Stud. Univ. Babeş-Bolyai Math. 55 (2010), 45-51. Zbl 1240.30037, MR 2764250 |
| Reference:
|
[3] Gupta, V. P., Jain, P. K.: Certain classes of univalent functions with negative coefficients.Bull. Aust. Math. Soc. 14 (1976), 409-416. Zbl 323.30016, MR 0414849, 10.1017/S0004972700025326 |
| Reference:
|
[4] Sălăgean, G. S.: 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. Zbl 0531.30009, MR 0738107, 10.1007/BFb0066543 |
| 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 |
| . |
