Geometric properties of a certain class of multivalent analytic functions associated with the second-order differential subordination

Yu-Qin Tao; Yi-Hui Xu; Rekha Srivastava; Jin-Lin Liu; Yu-Qin Tao; Yi-Hui Xu; Rekha Srivastava; Jin-Lin Liu

doi:10.3934/math.2021024

AIMS Mathematics

2021, Volume 6, Issue 1: 390-403. doi: 10.3934/math.2021024

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Geometric properties of a certain class of multivalent analytic functions associated with the second-order differential subordination

1.
Department of Mathematics, Maanshan Teacher's College, Maanshan 243000, People's Republic of China
2.
Department of Mathematics, Suqian College, Suqian 223800, People's Republic of China
3.
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
4.
Department of Mathematics, Yangzhou University, Yangzhou 225002, People's Republic of China

Received: 27 August 2020 Accepted: 12 October 2020 Published: 15 October 2020
MSC : Primary 30C45; Secondary 30C80

We investigate some geometric properties of the class $\mathcal{Q}_n(A, B, \alpha)$ which is defined by the second-order differential subordination and find the sharp lower bound on $|z| = r < 1$ for the following functional: $ \mathrm{Re}\left\{(1-\alpha)z^{1-p}f'(z) +\frac{\alpha}{p-1}z^{2-p}f''(z)\right\} $ over the class $\mathcal{Q}_n(A, B, 0)$.
- analytic functions,
- univalent functions,
- second-order differential subordination,
- sharp bound,
- Schwarz lemma,
- Carathéodory inequality
Citation: Yu-Qin Tao, Yi-Hui Xu, Rekha Srivastava, Jin-Lin Liu. Geometric properties of a certain class of multivalent analytic functions associated with the second-order differential subordination[J]. AIMS Mathematics, 2021, 6(1): 390-403. doi: 10.3934/math.2021024

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Abstract

We investigate some geometric properties of the class $\mathcal{Q}_n(A, B, \alpha)$ which is defined by the second-order differential subordination and find the sharp lower bound on $|z| = r < 1$ for the following functional: $ \mathrm{Re}\left\{(1-\alpha)z^{1-p}f'(z) +\frac{\alpha}{p-1}z^{2-p}f''(z)\right\} $ over the class $\mathcal{Q}_n(A, B, 0)$.

References

[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. Ser. B Engl. Ed., 32 (2012), 765-774.
[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. Real Acad. Cienc. Exactas Fís. Natur. Ser. A Mat., 113 (2019), 2001-2015. doi: 10.1007/s13398-018-0584-y
[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, Michigan Math. J., 28 (1981), 157-172. doi: 10.1307/mmj/1029002507
[10]	M. Nunokawa, H. M. Srivastava, N. Tuneski, B. Jolevska-Tuneska, Some Marx-Ströhhacker type results for a class of multivalent functions, Miskolc Math. Notes, 18 (2017), 353-364.
[11]	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
[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, N. E. Xu, D. G. Yang, Inclusion relations and convolution properties of a certain class of analytic functions associated with the Ruscheweyh derivatives, J. Math. Anal. Appl., 331 (2007), 686-700. doi: 10.1016/j.jmaa.2006.09.019
[16]	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.
[17]	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
[18]	Q. Khan, M. Arif, M. Raza, G. Srivastava, H. Tang, S. U. Rehman, Some applications of a new integral operator in q-analog for multivalent functions, Mathematics, 7 (2019), 1-13.

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