A new subclass $ \mathcal{G}_n(A, B, \lambda) $ of meromorphically multivalent functions defined by the first-order differential subordination is introduced. Some geometric properties of this new subclass are investigated. The sharp upper bound on $ |z| = r < 1 $ for the functional $ \mathrm{Re}\{(1-\lambda)z^pf(z)-\frac{\lambda}{p}z^{p+1}f'(z)\} $ over the class $ \mathcal{G}_n(A, B, 0) $ is obtained.
Citation: Ying Yang, Jin-Lin Liu. Some geometric properties of certain meromorphically multivalent functions associated with the first-order differential subordination[J]. AIMS Mathematics, 2021, 6(4): 4197-4210. doi: 10.3934/math.2021248
A new subclass $ \mathcal{G}_n(A, B, \lambda) $ of meromorphically multivalent functions defined by the first-order differential subordination is introduced. Some geometric properties of this new subclass are investigated. The sharp upper bound on $ |z| = r < 1 $ for the functional $ \mathrm{Re}\{(1-\lambda)z^pf(z)-\frac{\lambda}{p}z^{p+1}f'(z)\} $ over the class $ \mathcal{G}_n(A, B, 0) $ is obtained.
| [1] |
M. K. Aouf, J. Dziok, J. Sokól, On a subclass of strongly starlike functions, Appl. Math. Lett., 24 (2011), 27–32. doi: 10.1016/j.aml.2010.08.004
|
| [2] | N. E. Cho, H. J. Lee, J. H. Park, R. Srivastava, Some applications of the first-order differential subordinations, Filomat, 30 (2016), 1456–1474. |
| [3] |
S. Devi, H. M. Srivastava, A. Swaminathan, Inclusion properties of a class of functions involving the Dziok-Srivastava operator, Korean J. Math., 24 (2016), 139–168. doi: 10.11568/kjm.2016.24.2.139
|
| [4] |
J. Dziok, Classes of meromorphic functions associated with conic regions, Acta Math. Sci., 32 (2012), 765–774. doi: 10.1016/S0252-9602(12)60056-3
|
| [5] | Y. C. Kim, Mapping properties of differential inequalities related to univalent functions, Appl. Math. Comput., 187 (2007), 272–279. |
| [6] | J. L. Liu, Applications of differential subordinations for generalized Bessel functions, Houston J. Math., 45 (2019), 71–85. |
| [7] | J. L. Liu, R. Srivastava, Hadamard products of certain classes of $p$-valent starlike functions, Rev. R. Acad. Cienc. Exactas, Fis. Nat., 113 (2019), 2001–2015. |
| [8] |
S. Mahmood, J. Sokól, New subclass of analytic functions in conical domain associated with Ruscheweyh $q$-differential operator, Results Math., 71 (2017), 1345–1357. doi: 10.1007/s00025-016-0592-1
|
| [9] |
S. S. Miller, P. T. Mocanu, Differential subordinations and univalent functions, Mich. Math. J., 28 (1981), 157–171. doi: 10.1307/mmj/1029002507
|
| [10] |
M. Nunokawa, H. M. Srivastava, N. Tuneski, B. Jolevska-Tuneska, Some Marx-Strohhäcker type results for a class of multivalent functions, Miskolc Math. Notes, 18 (2017), 353–364. doi: 10.18514/MMN.2017.1952
|
| [11] | L. Shi, Q. Khan, G. Srivastava, J. L. Liu, M. Arif, A study of multivalent $q$-starlike functions connected with circular domain, Mathematics, 7 (2019), 1–12. |
| [12] |
H. M. Srivastava, M. K. Aouf, A. O. Mostafa, H. M. Zayed, Certain subordination-preserving family of integral operators associated with $p$-valent functions, Appl. Math. Inf. Sci., 11 (2017), 951–960. doi: 10.18576/amis/110401
|
| [13] |
H. M. Srivastava, R. M. El-Ashwah, N. Breaz, A certain subclass of multivalent functions involving higher-order derivatives, Filomat, 30 (2016), 113–124. doi: 10.2298/FIL1601113S
|
| [14] |
H. M. Srivastava, B. Khan, N. Khan, Q. Z. Ahmad, Coefficient inequalities for $q$-starlike functions associated with the Janowski functions, Hokkaido Math. J., 48 (2019), 407–425. doi: 10.14492/hokmj/1562810517
|
| [15] |
H. M. Srivastava, Operators of basic (or $q$-) calculus and fractional $q$-calculus and their applications in geometric function theory of complex analysis, Iran. J. Sci. Technol. Trans., A$:$ Sci., 44 (2020), 327–344. doi: 10.1007/s40995-019-00815-0
|
| [16] |
Y. Sun, Y. P. Jiang, A. Rasila, H. M. Srivastava, Integral representations and coefficient estimates for a subclass of meromorphic starlike functions, Complex Anal. Oper. Theory, 11 (2017), 1–19. doi: 10.1007/s11785-016-0531-x
|
Ying Yang, Jin-Lin Liu. Some geometric properties of certain meromorphically multivalent functions associated with the first-order differential subordination[J]. AIMS Mathematics, 2021, 6(4): 4197-4210. doi: 10.3934/math.2021248
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