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Certain subclasses of analytic functions with varying arguments associated with q-difference operator

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Abstract

In this paper, we introduce the new classes \(VE_{q}(n,\lambda ,\beta )\) and V\(G_{q}(n,\lambda ,\beta )\) of analytic functions with varying arguments defined by q-Al-Oboudi difference operator and study different properties for them.

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References

  1. Al-Oboudi, F.M.: On univalent functions defined by a generalized Sălăgean operator. Int. J. Math. Math. Sci 27, 1429–1436 (2004)

    Article  Google Scholar 

  2. Altinkaya, S., Magesh, N., Yalcin, S.: Construction of Toeplitz Matrices whose elements are the coefficients of univalent functions associated with \(q-\)derivative operator. Caspian J. Math. Sci. 8(1), 51–57 (2019)

    MATH  Google Scholar 

  3. Annby, M.H., Mansour, Z.S.: \(q\)-Fractional Calculus Equations. Lecture Notes in Mathematics, vol. 2056. Springer, Berlin (2012)

  4. Aouf, M.K.: Neighborhoods of certain classes of analytic functions with negative coefficients. Int. J. Math. Sci. 2006, Article ID 38258, 1–6 (2006)

  5. Aouf, M.K.: Subordination properties for a certain class of analytic functions defined by Sălăgeăn operator. Appl. Math. Lett. 22, 1581–1585 (2009)

    Article  MathSciNet  Google Scholar 

  6. Aouf, M.K.: A subclass of uniformly convex functions with negative coefficients. Math. Tome 52 75(2), 99–111 (2010)

    MathSciNet  MATH  Google Scholar 

  7. Aouf, M.K., Cho, N.E.: On a certain subclass of analytic functions with negative coefficients. Tr. J. Math. 22, 15–32 (1998)

    MathSciNet  MATH  Google Scholar 

  8. Aouf, M.K., Darwish, H.E., Sălăgeăn, G.S.: On a generalization of starlike functions with negative coefficients. Math. Tome 43 66(1), 3–10 (2001)

    MathSciNet  MATH  Google Scholar 

  9. Aouf, M.K., Mostafa, A.O.: Some properties of a subclass of uniformly convex functions with negative coefficients. Demonstr. Math. 41(2), 353–370 (2008)

    MathSciNet  MATH  Google Scholar 

  10. Aouf, M.K., Mostafa, A.O., Adwan, E.A.: Certain subclasses of analytic functions with varying arguments. Le Mat. 69, Fac. 1, 249–257 (2014)

  11. Aouf, M.K., Mostafa, A.O., AL-Quhali, F.Y.: Properties for class of \(\beta \)-uniformly univalent functions defined by type \(q\)-difference operator. Int. J. Open Probl. Complex Anal. 11(2), 1–16 (2019)

    Google Scholar 

  12. Aouf, M.K., Seoudy, T.M.: Convolution properties for classes of bounded analytic functions with complex order defined by q-derivative operator. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. 113(2), 1279–1288 (2019)

    Article  MathSciNet  Google Scholar 

  13. Aouf, M.K., Shamandy, A., Mostafa, A.O., El-Emam, F.: Subordination results associated with \(\beta \)-uniformly convex and starlike functions. Proc. Pak. Acad. Sci. 46(2), 97–101 (2009)

    MathSciNet  Google Scholar 

  14. Aral, A., Gupta, V., Agarwal, R.P.: Applications of q-Calculus in Operator Theory. Springer, New York (2013)

    Book  Google Scholar 

  15. Frasin, B.A., Murugusundaramoorthy, G.: A subordination results for a class of analytic functions defined by \(q-\)differential operator. Ann. Univ. Paedagog. Crac. Stud. Math. 19, 53–64 (2020)

    MathSciNet  Google Scholar 

  16. Gasper, G., Rahman, M.: Basic Hypergeometric Series. Combridge University Press, Cambrididge (1990)

    MATH  Google Scholar 

  17. Govindaraj, M., Sivasubramanian, S.: On a class of analytic function related to conic domains involving \(q\)-calculus. Anal. Math. 43(3), 475–487 (2017)

    Article  MathSciNet  Google Scholar 

  18. Jackson, F.H.: On q-functions and a certain difference operator. Trans. R. Soc. Edinb. 46, 253–281 (1908)

    Article  Google Scholar 

  19. Magesh, N., Altinkaya, S., Yalcin, S.: Certain subclasses of \( k\)-uniformly starlike functions associated with symmetric \(q\)-derivative operator. J. Comput. Anal. Appl. 24(8), 1464–1473 (2018)

    MathSciNet  Google Scholar 

  20. Nishiwaki, J., Owa, S.: Coefficient inequalities for certain analytic functions. Int. J. Math. Math. Sci. 29(5), 285–290 (2002)

    Article  MathSciNet  Google Scholar 

  21. Sălăgean, G.: Subclasses of Univalent Functions. Lecture Notes in Mathematics, vol. 1013. Springer, New York, pp. 362–372 (1983)

  22. Seoudy, T.M., Aouf, M.K.: Convolution properties for certain classes of analytic functions defined by q-derivative operator. Abstr. Appl. Anal. 2014, Article ID 846719, 1–7 (2014)

  23. Seoudy, T.M., Aouf, M.K.: Coefficient estimates of new classes of q-starlike and q-convex functions of complex order. J. Math. Inequal. 10(1), 135–145 (2016)

    Article  MathSciNet  Google Scholar 

  24. Silverman, H.: Univalent functions with varying arguments. Houston J. Math. 7(2), 283–287 (1981)

    MathSciNet  MATH  Google Scholar 

  25. Srivastava, H.M., Mostafa, A.O., Aouf, M.K., Zayed, H.M.: Basic and fractional q-calculus and associated Fekete–Szegö problem for p-valently q-starlike functions and p-valently q-convex functions of complex order. Miskolc Math. Notes 20(1), 489–509 (2019)

    Article  MathSciNet  Google Scholar 

  26. Uralegaddi, B.A., Ganigi, M.D., Sarangi, S.M.: Univalent functions with positive coefficients. Tamkang J. Math. 25(3), 225–230 (1994)

    MathSciNet  MATH  Google Scholar 

  27. Zayed, H.M., Aouf, M.K.: Subclasses of analytic functions of complex order associated with q-Mittag Leffler function. J. Egypt. Math. Soc. 26(2), 278–286 (2018)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors would like to thank the referees of the paper for their helpful suggestions.

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  1. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    M. K. Aouf, A. O. Mostafa & R. E. Elmorsy

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  1. M. K. Aouf
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  2. A. O. Mostafa
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  3. R. E. Elmorsy
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Correspondence to M. K. Aouf.

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Aouf, M.K., Mostafa, A.O. & Elmorsy, R.E. Certain subclasses of analytic functions with varying arguments associated with q-difference operator. Afr. Mat. 32, 621–630 (2021). https://doi.org/10.1007/s13370-020-00849-3

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