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Licensed Unlicensed Requires Authentication Published by De Gruyter October 20, 2018

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

  • Muhammed Arif EMAIL logo and Bakhtiar Ahmad
From the journal Mathematica Slovaca

Abstract

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.

MSC 2010: 30C45; 30C50
  1. Communicated by Stanisława Kanas

References

[1] ALDAWISH, I., DARUS, M.: Starlikness of q-differential operator involving quantum calculus, Korean J. Math. 22(4) (2014), 699–709.10.11568/kjm.2014.22.4.699Search in Google Scholar

[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.10.1155/2013/382312Search in Google Scholar

[3] ALDWEBY, H., DARUS, M.: Some subordination results on q-analogue of Ruscheweyh differential operator, Abstr. Appl. Anal. 2014, Article ID 958563, 6 pp.10.1155/2014/958563Search in Google Scholar

[4] ARAL, A.: On the generalized Picard and Gauss Weierstrass singular integrals, J. Compu. Anal. Appl. 8(3) (2006), 249–261.Search in Google Scholar

[5] ARAL, A., GUPTA, V.: Generalized q-Baskakov operators, Math. Slovaca 61(4) (2011), 619–634.10.2478/s12175-011-0032-3Search in Google Scholar

[6] ARAL, A., GUPTA, V.: On the Durrmeyer type modification of the q-Baskakov type operators, Nonlinear Anal. 72(3–4) (2010), 1171–1180.10.1016/j.na.2009.07.052Search in Google Scholar

[7] ARAL, A., GUPTA, V.: On q-Baskakov type operators, Demonstr. Math. 42(1) (2009), 109–122.10.1515/dema-2009-0111Search in Google Scholar

[8] ANASTASSIU, G. A., GAL, S. G.: Geometric and approximation properties of generalized singular integrals, J. Korean Math. Soci. 23(2) (2006), 425–443.10.4134/JKMS.2006.43.2.425Search in Google Scholar

[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.10.1155/JIA/2006/17231Search in Google Scholar

[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), 1–16.10.1016/S0252-9602(12)60106-4Search in Google Scholar

[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.Search in Google Scholar

[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.Search in Google Scholar

[13] JACKSON, F. H.: On q-definite integrals, Quart. J. Mech. Appl. Math. 41 (1910), 193–203.Search in Google Scholar

[14] JACKSON, F. H.: On q-functions and a certain difference operator, Proc. Roy. Soc. Edinburgh Sect. 46(2) (1909), 253–281.10.1017/S0080456800002751Search in Google Scholar

[15] KANAS, S., RĂDUCANU, D.: Some class of analytic functions related to conic domains, Math. Slovaca 64(5) (2014), 1183–1196.10.2478/s12175-014-0268-9Search in Google Scholar

[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.Search in Google Scholar

[17] MOHAMMED, A., DARUS, M.: A generalized operator involving the q-hypergeometric function, Mat. Vesnik 65(4) (2013), 454–465.Search in Google Scholar

[18] POMMERENKE, C.: On meromorphic starlike functions, Pacific J. Math. 13 (1963), 221–235.10.2140/pjm.1963.13.221Search in Google Scholar

[19] ROGOSINSKI, W.: On the coefficients of subordinate functions, Proc. Lond. Math. Soc. 48(2) (1943), 48–82.10.1112/plms/s2-48.1.48Search in Google Scholar

[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), 135–145.10.7153/jmi-10-11Search in Google Scholar

[21] URALEGADDI, B. A., SOMANATHA, C.: Certain differential operators for meromorphic functions, Houston J. Math. 17(2) (1991), 279–284.Search in Google Scholar

Received: 2017-03-01
Accepted: 2017-06-23
Published Online: 2018-10-20
Published in Print: 2018-10-25

© 2018 Mathematical Institute Slovak Academy of Sciences

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