Subclass of Bazilevič functions of complex order

Mohsan Raza; Khalida Inayat Noor; Mohsan Raza; Khalida Inayat Noor

doi:10.3934/math.2020162

AIMS Mathematics

2020, Volume 5, Issue 3: 2448-2460. doi: 10.3934/math.2020162

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Research article

Subclass of Bazilevič functions of complex order

Mohsan Raza ^{1
,
,},
Khalida Inayat Noor ²

1.
Department of Mathematics, Government College University, Faisalabad, Pakistan
2.
Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan

Received: 16 October 2019 Accepted: 26 February 2020 Published: 06 March 2020
MSC : 30C45, 30C50

In this paper, we define a class of analytic functions by using the concept of complex order. This class of analytic functions generalizes the class of Bazilevič functions. In the present work, we derive various useful properties and characteristics of this class such as coefficient bounds, Fekete-Szegö type inequality, arclength, integral preserving property, radius problem and some other interesting properties. Relevant connections of the results presented here with those obtained in earlier works are pointed.
- Bazilevič functions,
- complex order
Citation: Mohsan Raza, Khalida Inayat Noor. Subclass of Bazilevič functions of complex order[J]. AIMS Mathematics, 2020, 5(3): 2448-2460. doi: 10.3934/math.2020162

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Abstract

In this paper, we define a class of analytic functions by using the concept of complex order. This class of analytic functions generalizes the class of Bazilevič functions. In the present work, we derive various useful properties and characteristics of this class such as coefficient bounds, Fekete-Szegö type inequality, arclength, integral preserving property, radius problem and some other interesting properties. Relevant connections of the results presented here with those obtained in earlier works are pointed.

References

[1]	M. K. Aouf, T. M. Seoudy, Some properties of certain subclasses of p-valent Bazilevič functions associated with the generalized operator, Appl. Math. Lett., 24 (2011), 1953-1958. doi: 10.1016/j.aml.2011.05.029
[2]	A. A. Attiya, On a generalization class of bounded starlike functions of complex order, Appl. Math. Comp., 187 (2007), 62-67. doi: 10.1016/j.amc.2006.08.103
[3]	I. E. Bazilevič, On a class of integrability in quadratures of the Loewner-Kufarev equation, Math. Sb., 37 (1955), 471-476.
[4]	D. M. Campbell, K. Pearce, Generalized Bazilevič functions, Rocky Moun. J. Math., 9 (1979), 197-226. doi: 10.1216/RMJ-1979-9-2-197
[5]	N. E. Cho, V. Kumar, On a coefficient conjecture for Bazilevi č functions, Bull. Malays. Math. Sci. Soc., 2019.
[6]	N. E. Cho, Y. J. Sim, D. K. Thomas, On the difference of coefficients of Bazilevič functions, Comp. Meth. Fun. Theo., 19 (2019), 671-685. doi: 10.1007/s40315-019-00287-8
[7]	Q. Deng, On the coefficients of Bazilevič functions and circularly symmetric functions, Appl. Math. Lett., 24 (2011), 991-995. doi: 10.1016/j.aml.2011.01.012
[8]	A. W. Goodman, Univalent Functions, Mariner Publishing Company, 1983.
[9]	H. Irmak, T. Bulboacă, N. Tuneski, Some relations between certain classes consisting of α-convex type and Bazilević type functions, Appl. Math. Lett., 24 (2011), 2010-2014. doi: 10.1016/j.aml.2011.05.034
[10]	F. R. Keogh, E. P. Merks, A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc., 20 (1969), 8-12. doi: 10.1090/S0002-9939-1969-0232926-9
[11]	Y. C. Kim, A note on growth theorem of Bazilevič functions, Appl. Math. Comp., 208 (2009), 542-546. doi: 10.1016/j.amc.2008.12.027
[12]	Y. C. Kim, H. M. Srivastava, The Hardy space for a certain subclass of Bazilevič functions, Appl. Math. Comp., 183 (2006), 1201-1207. doi: 10.1016/j.amc.2006.06.044
[13]	S. S. Miller, P. T. Mocanu, Differential subordinations, Marcel Dekker, Inc., New York, Basel, 2000.
[14]	J. Sokół, D. K. Thomas, The fifth and sixth coefficients for Bazilevič functions B₁(α), Mediterr. J. Math., 14 (2017), 158.
[15]	M. A. Nasr, M. K. Aouf, Starlike function of complex order, J. Natur. Sci. Math., 25 (1985), 1-12.
[16]	K. I. Noor, On Bazilevič functions of complex order, Nihon. Math. J., 3 (1992), 115-124.
[17]	K. I. Noor, S. A. Al-Bany, On Bazilevič functions, Int. J. Math. Math. Sci., 10 (1987), 79-88. doi: 10.1155/S0161171287000103
[18]	K. I. Noor, S. Z. H. Bukhari, On analytic functions related with generalized Robertson functions, Appl. Math. Comput., 215 (2009), 2965-2970.
[19]	M. Raza, W. U. Haq, Rabia, On a subclass of Bazilevič functions, Math. Slovaca, 67 (2017), 1043-1053.
[20]	M. Raza, S. N. Malik, K. I. Noor, On some inequalities of certain class of analytic functions, J. Inequal. Appl., 2012 (2012), 1-15. doi: 10.1186/1029-242X-2012-1
[21]	R. Singh, On Bazilevič functions, Proc. Amer. Math. Soc., 38 (1973), 261-271.
[22]	E. T. Whittaker, G. N. Watson, A course of modern analysis, Cambridge Univ. Press, 1958.

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