International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

On q-Mocanu Type Functions Associated with q-Ruscheweyh Derivative Operator

  • Khalida Inayat Noor
  • Shujaat Ali Shah1*
  1. Department of Mathematics, COMSATS University Islamabad, Pakistan.

* Corresponding author

Abstract

In this paper, we introduce certain subclasses of analytic functions defined by using the q-difference operator. Mainly we give several inclusion results for defined classes. Also, certain applications due to q-Ruscheweyh derivative operator will be discussed.

How to Cite

K. I. Noor, S. A. Shah, On q-Mocanu Type Functions Associated with q-Ruscheweyh Derivative Operator, Int. J. Anal. Appl. 18 (2020), 550–558.

BibTeX
@article{Noor2020,
  author  = {Noor, Khalida Inayat and Shah, Shujaat Ali},
  title   = {On q-Mocanu Type Functions Associated with q-Ruscheweyh Derivative Operator},
  journal = {Int. J. Anal. Appl.},
  volume  = {18},
  year    = {2020},
  pages   = {550--558},
  doi     = {}
}

References

  • [1] O. Altintas, N. Mustafa, Coefficient bounds and distortion theorems for the certain analytic functions, Turk. J. Math. 43 (2019), 985-997.
  • [2] J. Dziok, Classes of functions associated with bounded Mocanu variation, J. Inequal. Appl. (2013), Art. ID 349.
  • [3] H. Exton, q-Hypergeometric functions and applications, Ellis Horwood Limited, UK, 1983.
  • [4] G. Gasper, M. Rahman, Basic hypergeometric series, Cambridge University Press, Cambridge, UK, 1990.
  • [5] H.A. Ghany, q-derivative of basic hypergeomtric series with respect to parameters, Int. J. Math. Anal. 3 (2009), 1617-1632.
  • [6] M.E.H. Ismail, E. Merkes, D. Styer, A generalization of starlike functions, Complex Var., Theory Appl. 14 (1990), 77-84.
  • [7] F.H. Jackson, On q-functions and a certain difference operator, Trans. R. Soc. Edin. 46 (1908), 253-281.
  • [8] S. Kanas, R. Raducanu, Some classes of analytic functions related to Conic domains, Math. Slovaca. 64 (2014), 1183-1196.
  • [9] V. Koc, P. Cheung, Quantum Calculus, Springer, 2001.
  • [10] S.S. Miller, P. T. Mocanu, Differential subordinations theory and applications, Marcel Dekker, New York, Basel, 2000.
  • [11] P.T. Mocanu, Une propriete de convexite generlise dans la theorie de la representation conforme, Math. (Cluj). 11 (1969), 127-133.
  • [12] M. Naeem, S. Hussain, T. Mahmood, S. Khan, M. Darus, A new subclass of analytic functions defined by using Salagean q-differential operator, Mathematics. 7 (2019), 458.
  • [13] K.I. Noor, On generalized q-close-to-convexity, Appl. Math. Inf. Sci. 11 (2017), 1383-1388.
  • [14] K.I. Noor, S. Hussain, On certain analytic functions associated with Ruscheweyh derivatives and bounded Mocanu variation, J. Math. Anal. Appl. 340 (2008), 1145-1152.
  • [15] K.I. Noor, S. Riaz, Generalized q-starlike functions, Stud. Sci. Math. Hungerica. 54 (2017), 509-522.
  • [16] S. Ruscheweyh, New criteria for univalent functions. Proc. Amer. Math. Soc. 49 (1975), 109-115.
  • [17] H. Shamsan, S. Latha, On genralized bounded Mocanu variation related to q-derivative and conic regions, Ann. Pure Appl. Math. 17 (2018), 67-83.
  • [18] H.E.O. Ucar, Coefficient inequality for q-starlike functions, Appl. Math. Comput. 276 (2016), 122-126.