New Subclass of Analytic Functions in Conical Domain Associated with Ruscheweyh q-Differential Operator

Article Sidebar

PDF
Cite as:
Shahid Khan, Saqib Hussain, Muhammad Asad Zaighum, Muhammad Mumtaz Khan, New Subclass of Analytic Functions in Conical Domain Associated with Ruscheweyh q-Differential Operator, Int. J. Anal. Appl., 16 (2) (2018), 239-253.

Main Article Content

Shahid Khan, Saqib Hussain, Muhammad Asad Zaighum, Muhammad Mumtaz Khan

Abstract

In this paper, we consider a new class of analytic functions which is defined by means of a Ruscheweyh q-differential operator. We investigated some new results such as coefficients inequalities and other interesting properties of this class. Comparison of new results with those that were obtained in earlier investigation are given as Corollaries.

Article Details

References

  1. N. I. Ahiezer, Elements of theory of elliptic functions, Moscow, 1970.
  2. S. Hussain, S. Khan, M. A. Zaighum and M. Darus, Certain subclass of analytic functions related with conic domains and associated with Salagean q-differential operator, AIMS Math. 2(4)(2017), 622-634.
  3. S. Hussain, S. Khan, M. A. Zaighum, M. Darus and Z. Shareef, Coefficients Bounds for Certain Subclass of Biunivalent Functions Associated with Ruscheweyh q-Differential Operator, J. Complex Anal. 2017 (2017), Article ID 2826514.
  4. W. Janowski, Some extremal problems for certain families of analytic functions, Ann. Polon. Math. 28 (1973) 297-326.
  5. S. Kanas, A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math, 105 (1999), 327-336.
  6. S. Kanas, A. Wisniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pures Appl. 45 (2000), 647-657.
  7. S. Kanas, D. Raducanu, Some class of analytic functions related to conic domains, Math. slovaca, 64(5) (2014), 1183-1196.
  8. F. R. Keogh, E. P. Merkes, A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc, 20 (1969), 8-12.
  9. N. Khan, B. Khan, Q. Z. Ahmad and S. Ahmad, Some Convolution Properties of Multivalent Analytic Functions, AIMS Math. 2 (2) (2017), 260-268.
  10. W. Ma, D. Minda, A unified treatment of some special classes of univalent functions. In: Proc. of the Conference on Complex Analysis (Tianjin), 1992 (Z. Li, F. Y. Ren, L. Yang, S. Y. Zhang, eds.), Conf. Proc. Lecture Notes Anal., Vol. 1, Int. Press, Massachusetts, 1994, 157-169.
  11. K. I. Noor, S. N. Malik, On coefficient inequalities of functions associated with conic domains, Comput. Math. Appl, 62(2011), 2209-2217.
  12. K. I. Noor, J. Sokol and Q. Z. Ahmad, Applications of conic type regions to subclasses of meromorphic univalent functions with respect to symmetric points, Rev. R. Acad. Cienc. Exactas Fs. Nat., Ser. A Mat. 111 (2017), 947C958.
  13. K. I. Noor, J. Sokól and Q. Z. Ahmad, Applications of the diffierential operator to a class of meromorphic univalent functions. J. Egyptian Math. Soc. 24 (2) (2016), 181-186.
  14. M. Nunokawa, S. Hussain, N. Khan and Q. Z. Ahmad, A subclass of analytic functions related with conic domain, J. Clas. Anal. 9 (2016), 137-149.
  15. W. Rogosinski, On the coefficients of subordinate functions, Proc. Lond. Math. Soc, 48 (1943), 48-82.
  16. S. T. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc, 49 (1975), 109-115.
  17. H. Selverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc, 51 (1975), 109-116.
  18. S. Shams, S. R. Kulkarni, J. M. Jahangiri, Classes of uniformly starlike and convex functions, Int. J. Math. Math. Sci, 55 (2004) 2959-2961.