Fractional q-differintegral operator related to univalent functions with negative coefficients

Document Type : Research Paper

Author

Department of Mathematics, Payame Noor University, Tehran, Iran

10.22103/jmmrc.2020.13685.1084

Abstract

In this paper, we introduce a new subfamily of univalent functions defined in the
open unit disk involving a fractional q-differintegral operator. Some results on
coefficient estimates, weighted mean, convolution structure and convexity are discussed

Keywords


[1] P. Ravi Agarwal, Certain fractional q{integrals and q{derivatives, Mathematical Proceedings of the Cambridge Philosophical Society, 66, 2 (1969) 365-370.
[2] A. Aral, V. Gupta, P. Ravi Agarwal, Applications of q{calculus in operator theory, Springer, 2013.
[3] G. Gasper, M. Rahman, G. George, Basic hypergeometric series, Cambridge university press, vol. 66, 2004.
[4] F. H. Jackson, On q-functions and a certain di erence operator, Transactions of the Royal Society of  Edinburgh Earth Sciences, 46, 2 (1908), 253-281.
[5] S. D. Purohit, R. K. Raina, Certain subclasses of analytic functions associated with fractional q{calculus operators, Mathematica Scandinavica, (2011), 55-70.
[6] R. K. Raina, H. M. Srivastava, Some subclasses of analytic functions associated with fractional calculus operators, Computers & Mathematics with Applications, 37, 9 (1999), 73-84.
[7] P. M. Rajkovic, S. D. Marinkovic, M. S. Stankovic, Fractional integrals and derivatives in q{calculus,  Applicable analysis and discrete mathematics, (2007), 311-323.
[8] H. M. Srivastava, M. K. Aouf, A certain fractional derivative operator and its applications to a new class of analytic and multivalent functions with negative coecients, Journal of Mathematical Analysis and Applications, 171, 1 (1992), 1-13.