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

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].

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  • 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.