ESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF SUBCLASS OF BI-UNIVALENT FUNCTIONS INVOLVING THE Q- DERIVATIVE OPERATOR

Pramila Vıjaywargıya; Lokesh Vıjayvergy

doi:10.1501/Commua1_0000000789

ESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF SUBCLASS OF BI-UNIVALENT FUNCTIONS INVOLVING THE Q- DERIVATIVE OPERATOR

Yıl 2017, Cilt: 66 Sayı: 1, 199 - 205, 01.02.2017

Pramila Vıjaywargıya Lokesh Vıjayvergy

https://doi.org/10.1501/Commua1_0000000789

Öz

In this paper, estimates for second and third MacLaurin coefficients of a new subclass of analytic and bi-univalent functions in the open unit disk are determined, and certain special cases are also indicated

Anahtar Kelimeler

Univalent functions, bi-univalent functions, bi-starlike function, biconvex function, functions with bounded boundary rotation, coffecient estimates, q-derivativeoperator

Kaynakça

A. Aral, V. Gupta and R.P.Agrawal, Applications of q-calculus in Operator Theory, Springer, New York, USA, 2013.
D. A. Brannan and T. S. Taha, On some classes of bi-univalent functions, Stud. Univ. Babe¸s- Bolyai Math., 31(1986), no. 2, 70–77.
P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften Series, , Springer Verlag, New York, 1983.
B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., (2011), no. 9, 1569–1573.
S. P. Goyal and P. Goswami, Estimate for initial Maclaurin coe¢ cients of bi-univalent func- tions for a class de…ned by fractional derivatives, J. Egyptian Math. Soc., 20(3)(2012), 179–
F. H. Jackson, On q-de…nite integrals, Quarterly J. Pure Appl. Math. 41 (1910), 193-203.
F. H. Jackson, On q-functions and a certain diğerence operator, Transactions of the Royal Society of Edinburgh 46 (1908), 253-281.
V. Paatero, Uber die konforme Abbildung von Gebieten deren Rander von beschrÃxonkter Drehung sind, Ann. Acad. Sci. Fenn. Ser. A33 No. 9 (1931).
K. Padmanabhan and R. Parvatham, Properties of a class of functions with bounded bound- ary rotation, Ann. Polon. Math., 31(1975), 311–323.
B. Pinchuk, Functions with bounded boundary rotation, Israel J. Math., 10(1971), 7–16.
H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi- univalent functions, Appl. Math. Lett., 23(2010), no. 10, 1188–1192.
Q.-H. Xu, Y.-C. Gui and H.M. Srivastava, Coe¢ cient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett.25 (2012) 990-994.
Q.-H. Xu, H.-G. Xiao and H.M. Srivastava, A certain general subclass of analytic and biu- nivalent functions and associated coe¢ cient estimate problems, Appl. Math. Comput. 218 (2012) 11461165.

Yıl 2017, Cilt: 66 Sayı: 1, 199 - 205, 01.02.2017

Pramila Vıjaywargıya Lokesh Vıjayvergy

https://doi.org/10.1501/Commua1_0000000789

Öz

Kaynakça

A. Aral, V. Gupta and R.P.Agrawal, Applications of q-calculus in Operator Theory, Springer, New York, USA, 2013.
D. A. Brannan and T. S. Taha, On some classes of bi-univalent functions, Stud. Univ. Babe¸s- Bolyai Math., 31(1986), no. 2, 70–77.
P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften Series, , Springer Verlag, New York, 1983.
B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., (2011), no. 9, 1569–1573.
S. P. Goyal and P. Goswami, Estimate for initial Maclaurin coe¢ cients of bi-univalent func- tions for a class de…ned by fractional derivatives, J. Egyptian Math. Soc., 20(3)(2012), 179–
F. H. Jackson, On q-de…nite integrals, Quarterly J. Pure Appl. Math. 41 (1910), 193-203.
F. H. Jackson, On q-functions and a certain diğerence operator, Transactions of the Royal Society of Edinburgh 46 (1908), 253-281.
V. Paatero, Uber die konforme Abbildung von Gebieten deren Rander von beschrÃxonkter Drehung sind, Ann. Acad. Sci. Fenn. Ser. A33 No. 9 (1931).
K. Padmanabhan and R. Parvatham, Properties of a class of functions with bounded bound- ary rotation, Ann. Polon. Math., 31(1975), 311–323.
B. Pinchuk, Functions with bounded boundary rotation, Israel J. Math., 10(1971), 7–16.
H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi- univalent functions, Appl. Math. Lett., 23(2010), no. 10, 1188–1192.
Q.-H. Xu, Y.-C. Gui and H.M. Srivastava, Coe¢ cient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett.25 (2012) 990-994.
Q.-H. Xu, H.-G. Xiao and H.M. Srivastava, A certain general subclass of analytic and biu- nivalent functions and associated coe¢ cient estimate problems, Appl. Math. Comput. 218 (2012) 11461165.

Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Bölüm	Research Article
Yazarlar	Pramila Vıjaywargıya Bu kişi benim Lokesh Vıjayvergy Bu kişi benim
Yayımlanma Tarihi	1 Şubat 2017
Yayımlandığı Sayı	Yıl 2017 Cilt: 66 Sayı: 1

Kaynak Göster

APA	Vıjaywargıya, P., & Vıjayvergy, L. (2017). ESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF SUBCLASS OF BI-UNIVALENT FUNCTIONS INVOLVING THE Q- DERIVATIVE OPERATOR. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(1), 199-205. https://doi.org/10.1501/Commua1_0000000789
AMA	Vıjaywargıya P, Vıjayvergy L. ESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF SUBCLASS OF BI-UNIVALENT FUNCTIONS INVOLVING THE Q- DERIVATIVE OPERATOR. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2017;66(1):199-205. doi:10.1501/Commua1_0000000789
Chicago	Vıjaywargıya, Pramila, ve Lokesh Vıjayvergy. “ESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF SUBCLASS OF BI-UNIVALENT FUNCTIONS INVOLVING THE Q- DERIVATIVE OPERATOR”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, sy. 1 (Şubat 2017): 199-205. https://doi.org/10.1501/Commua1_0000000789.
EndNote	Vıjaywargıya P, Vıjayvergy L (01 Şubat 2017) ESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF SUBCLASS OF BI-UNIVALENT FUNCTIONS INVOLVING THE Q- DERIVATIVE OPERATOR. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 1 199–205.
IEEE	P. Vıjaywargıya ve L. Vıjayvergy, “ESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF SUBCLASS OF BI-UNIVALENT FUNCTIONS INVOLVING THE Q- DERIVATIVE OPERATOR”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 66, sy. 1, ss. 199–205, 2017, doi: 10.1501/Commua1_0000000789.
ISNAD	Vıjaywargıya, Pramila - Vıjayvergy, Lokesh. “ESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF SUBCLASS OF BI-UNIVALENT FUNCTIONS INVOLVING THE Q- DERIVATIVE OPERATOR”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/1 (Şubat 2017), 199-205. https://doi.org/10.1501/Commua1_0000000789.
JAMA	Vıjaywargıya P, Vıjayvergy L. ESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF SUBCLASS OF BI-UNIVALENT FUNCTIONS INVOLVING THE Q- DERIVATIVE OPERATOR. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:199–205.
MLA	Vıjaywargıya, Pramila ve Lokesh Vıjayvergy. “ESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF SUBCLASS OF BI-UNIVALENT FUNCTIONS INVOLVING THE Q- DERIVATIVE OPERATOR”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 66, sy. 1, 2017, ss. 199-05, doi:10.1501/Commua1_0000000789.
Vancouver	Vıjaywargıya P, Vıjayvergy L. ESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF SUBCLASS OF BI-UNIVALENT FUNCTIONS INVOLVING THE Q- DERIVATIVE OPERATOR. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(1):199-205.