Meromorphic functions with missing coefficients defined by $q$-derivative

Document Type : Research Paper

Authors

1 Department of Mathematics, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran

2 Department of Mathematics, Urmia University, Urmia, Iran

Abstract

By considering a fixed point in the punctured unit disk and using the $q$--derivative, a new subfamily of meromorphic and univalent functions is defined. Also, the first and second order {$q$--derivative} of meromorphic functions are introduced. Coefficient bounds, extreme points, radii of starlikeness and convexity are obtained. Furthermore, the convexity and preserving under convolution with some restrictions on parameters are investigated

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References

[1] G. Gasper, M. Rahman, and G. George, Basic hypergeometric series, Cambridge university press, 2004.
[2] Z. S. Mansour, Linear sequential q-di erence equations of fractional order, Fract. Calc. Appl. Anal vol. 12, no. 2 (2009) 159-178.
[3] G. Murugusundaramoorthy, K. Vijaya, and T. Janani, Subclasses of Starlike Functions with A Fixed Point involving q-hypergeometric function, J. Ana. Num. Theor. vol. 4, no. 1 (2016) 41{47.
[4] Sh. Najafzadeh, A. Ebadian, and Gordji, M. Eshaghi Certain subclasses of convex functions with positive and missing coecients by using a  xed point, The Journal of Non-linear Sciences and its Applications vol. 2, no. 4 (2009) 219-224.
[5] Sh. Najafzadeh, Fractional q-di erintegral operator related to univalent functions with negative coecients, J. Mahani Math. Research Center, vol. 9, no. 2 (2020) 69-77.

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History

  • Receive Date: 10 August 2022
  • Revise Date: 13 March 2023
  • Accept Date: 03 April 2023

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