Convolution Properties for Salagean-type Analytic Functions Defined by q- Difference Operator

Year 2019, Volume: 68 Issue: 2, 1647 - 1652, 01.08.2019

Asena Çetinkaya

https://doi.org/10.31801/cfsuasmas.420820

https://izlik.org/JA85UW27LY

Abstract

In this paper, we define  Salagean-type analytic  functions by using concept of q- derivative operator. We investigate convolution properties and coefficient estimates for Salagean-type analytic functions denoted by S^{m,\lambda}_q[A,B].

Keywords

salagean differential operator , q-difference operator , convolution

References

• Andrews, G. E., Applications of basic hypergeometric functions, SIAM Rev. 16 (1974), 441-484.
• Çaglar, M. and Deniz, E., Initial coefficients for a subclass of bi-univalent functions defined by Salagean differential operator, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 66 (1) (2017), 85-91. Fine, N. J., Basic hypergeometric series and applications, Math. Surveys Monogr. 1988.
• Gasper, G. and Rahman, M., Basic hypergeometric series, Cambridge University Press, 2004.
• Goodman, A. W., Univalent functions, Volume I and Volume II, Mariner Pub. Co. Inc. Tampa Florida, 1984.
• Jackson, F. H., On q- functions and a certain difference operator, Trans. Royal Soc. Edinburgh, 46 (1909), 253-281.
• Jackson, F. H., q- difference equations, Amer. J. Math. 32 (1910), 305-314.
• Janowski, W., Some extremal problems for certain families of analytic Functions I, Ann. Polon. Math. 28 (1973), 297-326.
• Kac, V. and Cheung, P., Quantum calculus, Springer, 2002.
• Salagean, G. S., Subclass of univalent functions, Complex Analysis-Fifth Romanian Finish Seminar, Bucharest, 1 (1998), 362-372.