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

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Khalida Inayat Noor
Shujaat Ali Shah

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.

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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.