A certain subclass of bi-univalent functions associated with Bell numbers and $q-$Srivastava Attiya operator

Erhan Deniz; Muhammet Kamali; Semra Korkmaz; Erhan Deniz; Muhammet Kamali; Semra Korkmaz

doi:10.3934/math.2020464

AIMS Mathematics

2020, Volume 5, Issue 6: 7259-7271. doi: 10.3934/math.2020464

Previous Article Next Article

Research article

A certain subclass of bi-univalent functions associated with Bell numbers and $q-$Srivastava Attiya operator

1.
Kafkas University, Faculty of Science and Letters, Department of Mathematics, Kars, Turkey
2.
Kyrgyz-Turkish Manas University, Faculty of Sciences, Department of Mathematics, Chyngyz Aitmatov avenue, Bishkek, Kyrgyz Republic

Received: 04 June 2020 Accepted: 31 August 2020 Published: 17 September 2020
MSC : 30C45, 30C50

In the present study, we introduced general a subclass of bi-univalent functions by using the Bell numbers and $q-$Srivastava Attiya operator. Also, we investigate coefficient estimates and famous Fekete-Szegö inequality for functions belonging to this interesting class.
- bi-univalent function,
- $q-$Srivastava Attiya operator,
- Bell numbers,
- coefficient estimates
Citation: Erhan Deniz, Muhammet Kamali, Semra Korkmaz. A certain subclass of bi-univalent functions associated with Bell numbers and $q-$Srivastava Attiya operator[J]. AIMS Mathematics, 2020, 5(6): 7259-7271. doi: 10.3934/math.2020464

Related Papers:

Abstract

In the present study, we introduced general a subclass of bi-univalent functions by using the Bell numbers and $q-$Srivastava Attiya operator. Also, we investigate coefficient estimates and famous Fekete-Szegö inequality for functions belonging to this interesting class.

References

[1]	E. T. Bell, The iterated exponential integers, Ann. Math., 39 (1938), 539-557.
[2]	E. T. Bell, Exponential polynomials, Ann. Math., 35 (1934), 558-577.
[3]	D. A. Brannan, J. G. Clunie, Aspects of Contemporary Complex Analysis, (Proceedings of the NATO Advanced Study Institute heald at the University of Durham, Durham; July 1-20, 1979), Academic Press: New York, NY, USA; London, UK, 1980.
[4]	D. A. Brannan, T. S. Taha, On some classes of bi-unvalent functions, Stud. Univ. Babeş-Bolyai Math., 31 (1986), 70-77.
[5]	N. E. Cho, S. Kumar, V. Kumar, et al. Starlike functions related to the Bell numbers, Symmetry, 219 (2019), 1-17.
[6]	M. Çaǧlar, E. Deniz, Initial coefficients for a subclass of bi-univalent functions defined by Salagean differential operator, Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat., 66 (2017), 85-91.
[7]	E. Deniz, Certain subclasses of bi-univalent functions satisfying subordinate conditions, J. Class. Anal., 2 (2013), 49-60.
[8]	P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, 259, Springer, New York, 1983.
[9]	H. Exton, q-Hypergeometric Functions and Applications, Chichester, UK: Ellis Horwood Limited, 1983.
[10]	B. A. Frasin, M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24 (2011), 1569-1573.
[11]	G. Gasper, M. Rahman, Basic Hypergeometric Series, Cambridge, UK: Cambridge University Press, 1990.
[12]	H. A. Ghany, q-derivative of basic hypergeomtric series with respect to parameters, Int. J. Math. Anal., 3 (2009), 1617-1632.
[13]	F. H. Jackson, On q-functions and a certain difference operator, Trans. Royal Society Edinburgh, 46 (1908), 253-281.
[14]	V. Kumar, N. E. Cho, V. Ravichandran, et al. Sharp coefficient bounds for starlike functions associated with the Bell numbers, Math. Slovaca, 69 (2019), 1053-1064.
[15]	A. Y. Lashin, Coefficient estimates for two subclasses of analytic and bi-Univalent functions, Ukr. Math. J., 70 (2019), 1484-1492.
[16]	M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Am. Math. Soc., 18 (1967), 63-68.
[17]	R. J. Libera, E. J. Zlotkıewicz, Coefficient bounds for the inverse of a function with derivatives in P, Proc. Amer. Math. Soc., 87 (1983), 251-257.
[18]	K. I. Noor, S. Riaz, M. A. Noor, On q-Bernardi integral operator, TWMS J. Pure Appl. Math., 8 (2017), 3-11.
[19]	E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in\|z\|< 1, Arch. Ration. Mech. Anal., 32 (1969), 100-112. doi: 10.1007/BF00247676
[20]	H. Orhan, N. Magesh, V. K. Balaji, Fekete-Szegö problem for certain classes of Ma-Minda bi-univalent functions, Afr. Math., 27 (2016), 889-897.
[21]	S. A. Shah, K. I. Noor, Study on the q-analogue of a ceratin family of linear operators, Turk J. Math., 43 (2019), 2707-2714.
[22]	H. M. Srivastava, A. A. Attiya, An integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination, Integ. Transf. Spec. F., 18 (2007), 207-216.
[23]	H. M. Srivastava, J. Choi, Series associated with zeta and related function, Dordrecht, the Netherlands: Kluwer Academic Publisher, 2001.
[24]	H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23 (2010), 1188-1192.
[25]	H. M. Srivastava, S. S. Eker, R. M. Ali, Coefficient bounds for a certain class of analytic and bi-univalent functions, Filomat, 29 (2015), 1839-1845.
[26]	Q. H. Xu, Y. C. Gui, H. M. Srivastava, Coefficient estimates for certain subclasses of analytic functions of complex order, Taiwanese J. Math., 15 (2011), 2377-2386.
[27]	Q. H. Xu, Y. C. Gui, H. M. Srivastava, Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett., 25 (2012), 990-994.
[28]	Q. H. Xu, H. G. Xiao, H. M. Srivastava, A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput., 218 (2012), 11461-11465.
[29]	P. Zaprawa, Estimates of Initial Coefficients for Bi-Univalent Functions, Abst. Appl. Anal. Article ID 357480, 6. 2014.
[30]	P. Zaprawa, On the Fekete-Szegö problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin, 21 (2014), 169-178.

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)