New subfamily of meromorphic multivalent starlike functions in circular domain involving q-differential operator

  • 1 Department of Mathematics, 23200, Mardan, Pakistan
Muhammed Arif
  • Corresponding author
  • Department of Mathematics, Abdul Wali Khan University Mardan, 23200, Mardan, Pakistan
  • Email
  • Search for other articles:
  • degruyter.comGoogle Scholar
and Bakhtiar Ahmad


The main object of the present paper is to investigate a number of useful properties such as sufficiency criteria, distortion bounds, coefficient estimates, radius of starlikness and radius of convexity for a new subclass of meromorphic multivalent starlike functions, which are defined here by means of a newly defined q-linear differential operator.

  • [1]

    ALDAWISH, I., DARUS, M.: Starlikness of q-differential operator involving quantum calculus, Korean J. Math. 22(4) (2014), 699–709.

  • [2]

    ALDWEBY, H., DARUS, M.: A subclass of harmonic univalent functions associated with q-analogue of Dziok-Srivastava operator, ISRN Appl. Math. 2013, Article ID 382312, 6 pp.

  • [3]

    ALDWEBY, H., DARUS, M.: Some subordination results on q-analogue of Ruscheweyh differential operator, Abstr. Appl. Anal. 2014, Article ID 958563, 6 pp.

  • [4]

    ARAL, A.: On the generalized Picard and Gauss Weierstrass singular integrals, J. Compu. Anal. Appl. 8(3) (2006), 249–261.

  • [5]

    ARAL, A., GUPTA, V.: Generalized q-Baskakov operators, Math. Slovaca 61(4) (2011), 619–634.

  • [6]

    ARAL, A., GUPTA, V.: On the Durrmeyer type modification of the q-Baskakov type operators, Nonlinear Anal. 72(3–4) (2010), 1171–1180.

  • [7]

    ARAL, A., GUPTA, V.: On q-Baskakov type operators, Demonstr. Math. 42(1) (2009), 109–122.

  • [8]

    ANASTASSIU, G. A., GAL, S. G.: Geometric and approximation properties of generalized singular integrals, J. Korean Math. Soci. 23(2) (2006), 425–443.

  • [9]

    ANASTASSIU, G. A., GAL, S. G.: Geometric and approximation properties of some singular integrals in the unit disk, J. Inequal. Appl. 2006, Article ID 17231, 19 pp.

  • [10]

    DZIOK, J., MURUGUSUNDARAMOORTHY, G., SOKOÅ, J.: On certain class of meromorphic functions with positive coefficients, Acta Math. Sci. Ser. B, Engl. Ed. 32(4) (2012), 1–16.

  • [11]

    GANIGI, M. R., URALEGADDI, B. A.: New criteria for meromorphic univalent functions, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 33(81) (1989), 9–13.

  • [12]

    HUDA, A., DARUS, M.: Integral operator defined by q-analogue of Liu-Srivastava operator, Stud. Univ. Babes-Bolyai Math. 58(4) (2013), 529–537.

  • [13]

    JACKSON, F. H.: On q-definite integrals, Quart. J. Mech. Appl. Math. 41 (1910), 193–203.

  • [14]

    JACKSON, F. H.: On q-functions and a certain difference operator, Proc. Roy. Soc. Edinburgh Sect. 46(2) (1909), 253–281.

  • [15]

    KANAS, S., RĂDUCANU, D.: Some class of analytic functions related to conic domains, Math. Slovaca 64(5) (2014), 1183–1196.

  • [16]

    LIU, M. S.: On a subclass of p-valent close to convex functions of type α and order β,, J. Math. Study 30(1) (1997) (Chinese), 102–104.

  • [17]

    MOHAMMED, A., DARUS, M.: A generalized operator involving the q-hypergeometric function, Mat. Vesnik 65(4) (2013), 454–465.

  • [18]

    POMMERENKE, C.: On meromorphic starlike functions, Pacific J. Math. 13 (1963), 221–235.

  • [19]

    ROGOSINSKI, W.: On the coefficients of subordinate functions, Proc. Lond. Math. Soc. 48(2) (1943), 48–82.

  • [20]

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

  • [21]

    URALEGADDI, B. A., SOMANATHA, C.: Certain differential operators for meromorphic functions, Houston J. Math. 17(2) (1991), 279–284.

Purchase article
Get instant unlimited access to the article.
Log in
Already have access? Please log in.

Journal + Issues

Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process.