Title: New Subfamily of Meromorphic Convex Functions in Circular Domain Involving q-Operator
Author(s): Bakhtiar Ahmad, Muhammad Arif
Pages: 75-82
Cite as:
Bakhtiar Ahmad, Muhammad Arif, New Subfamily of Meromorphic Convex Functions in Circular Domain Involving q-Operator, Int. J. Anal. Appl., 16 (1) (2018), 75-82.

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 convex functions, which are defined here by means of a newly defined q-linear differential operator.

Full Text: PDF

 

References


  1. I. Aldawish and M. Darus, Starlikness of q-differential operator involving quantum calculus, Korean J. Math., 22(4)(2014), 699 − 709. Google Scholar

  2. H. Aldweby and M. Darus, A subclass of harmonic univalent functions associated with q-analogue of Dziok-Srivastava operator, ISRN Math. Anal., 2013(2013), Article ID 382312, 6 pages. Google Scholar

  3. H. Aldweby and M. Darus, Some subordination results on q-analogue of Ruscheweyh differential operator, Abstr. Appl. Anal., 2014(2014), Article ID 958563, 6 pages. Google Scholar

  4. A. Aral, On the generalized Picard and Gauss Weierstrass singular integrals, J. Compu. Anal. Appl., 8(3)(2006), 249−261. Google Scholar

  5. A. Aral and V. Gupta, Generalized q-Baskakov operators, Math. Slovaca, 61(4)(2011), 619 − 634. Google Scholar

  6. A. Aral and V. Gupta, On the Durrmeyer type modification of the q-Baskakov type operators, Non-linear Anal. Theory, Methods and Appl., 72(3 − 4)(2010), 1171 − 1180. Google Scholar

  7. A. Aral and V. Gupta, On q-Baskakov type operators, Demonstratio Mathematica, 42(1)(2009), 109 − 122. Google Scholar

  8. G. A. Anastassiu and S. G. Gal, Geometric and approximation properties of generalized singular integrals, J. Korean Math. Soci., 23(2)(2006), 425 − 443. Google Scholar

  9. G. A. Anastassiu and S. G. Gal, Geometric and approximation properties of some singular integrals in the unit disk, J. Inequ. Appl., 2006(2016), Article ID 17231, 19 pages. Google Scholar

  10. J. Dziok, G. Murugusundaramoorthy and J. Soko l, On certain class of meromorphic functions with positive coefcients, Acta Mathematica Scientia B, 32(4)(2012), 1 − 16. Google Scholar

  11. M. R. Ganigi and B. A. Uralegaddi, New criteria for meromorphic univalent functions, Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 33(81)(1989), 9 − 13. Google Scholar

  12. A. Huda and M. Darus, Integral operator defined by q-analogue of Liu-Srivastava operator, Studia Univ. Babes-Bolyai Ser. Math. 58(4)(2013), 529 − 537. Google Scholar

  13. F. H. Jackson, On q-definite integrals, The Quarterly J. Pure Appl. Math., 41(1910), 193 − 203. Google Scholar

  14. F. H. Jackson, On q-functions and a certain difference operator, Trans. Royal Soc. Edinburgh, 46(2)(1909), 253 − 281. Google Scholar

  15. S. Kanas and D. R˘ aducanu, Some class of analytic functions related to conic domains, Math. Slovaca 64(5)(2014), 1183 − 1196. Google Scholar

  16. M. S. Liu, On a subclass of p-valent close to convex functions of type α and order β, J. Math. Study, 30(1)(1997), 102−104 (Chinese) Google Scholar

  17. A. Mohammed and M. Darus, A generalized operator involving the q-hypergeometric function, Mat. Vesnik, 65(4)(2013), 454 − 465. Google Scholar

  18. C. Pommerenke, On meromorphic starlike functions, Pac. J. Math. 13(1963), 221 − 235. Google Scholar

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

  20. B. A. Uralegaddi and C. Somanatha, Certain diferential operators for meromorphic functions, Houston J. Math. 17(2)(1991), 279 − 284. Google Scholar