Meromorphic Starlike Functions with Respect to Symmetric Points

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Muhammad Ghaffar Khan, Maslina Darus, Bakhtiar Ahmad, Gangadharan Murugusundaramoorthy, Raees Khan, Nasir Khan, Meromorphic Starlike Functions with Respect to Symmetric Points, Int. J. Anal. Appl., 18 (6) (2020), 1037-1047.

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Muhammad Ghaffar Khan, Maslina Darus, Bakhtiar Ahmad, Gangadharan Murugusundaramoorthy, Raees Khan, Nasir Khan

Abstract

The main purpose of this article is to introduce a class of meromorphic functions associated with the symmetric points in circular domain. We investigate the necessary and sufficient conditions, distortions theorem for this class. Furthermore, we obtain closure and convolutions properties, radii of starlikeness and partial sum results for these functions.

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References

  1. S. S. Miller and P. T.Mocanu, Second order differential inequalities in the complex plane, J. Math. Anal. Appl. 65 (1978), 289-305.
  2. S. S. Miller and P. T.Mocanu, Differential Subordinations, Theory and Applications, Series on Monographs and Textbooks in Pure and Appl. Math. No. 225, Marcel Dekker Inc., New York, 2000.
  3. R. M. Ali and V. Ravichandran, Class of meromorphic α-convex functions, Taiwan. J. Math. 14 (2010), 1479-1490.
  4. A. A. Catas, note on meromorphic m-valent starlike functions, J. Math. Inequal. 4 (2010), 601-607.
  5. O. S. Kwon and N. E. Cho, A class of nonlinear operators preservimg double subordinations, Abstr. Appl. Anal. 2018 (2008), 792160.
  6. K. I. Noor and F. Amber, On certain classes of meromorphic functions associated with conic domains, Abstr. Appl. Anal. 2012 (2012), ID 7921601.
  7. M. Nunokawa and O. P. Ahuja, On meromorphic starlike and convex functions, Indian J. Pure Appl. Math. 32 (2001), 1027-1032.
  8. M. Nunokawa, N. Owa, N. Uyanik and H. Shiraishi, Sufficient conditions for starlikeness of order α for meromorphic functions, Mathematical and Computer Modelling, Indian J. Pure Appl. Math. 55 (2012), 1245-1250.
  9. H. Tang, G. T. Deng and S. H. Li, On a certain new subclass of meromorphic close-to-convex functions, J. Inequal. Appl. 2013 (2013), 164.
  10. Z. G. Wang, Z. H. Liu and R. G. Xaing, Some criteria for meromorphic multivalent starlike functions, Appl. Math. Comput. 218 (2011), 1107-1111.
  11. Z. G. Wang, Y. Sun and N. Xu, certain properties of meromorphic close-to-convex functions, Appl. Math. Lett. 25 (2012), 454-460.
  12. Z. G. Wang, H. M. Serivastava and S. M Yuan, Some basic properties of certain subclasses of meromorphically starlike functions, J. Inequal. Appl. 2014 (2014), 29.
  13. D. J. Hallenbeck and S. Ruscheweyh, Subordination by convex functions, Proc. Amer. Math. Soc. 52 (1975), 191-195.
  14. K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan. 2 (1959), 72-75.
  15. N. E. Cho and S. Owa, Partial sums of certain meromorphic functions, J. Inequal. Pure Appl. Math. 5 (2004), 30.
  16. S. Sivaprasad, V. Ravichandran and G. Murugusundaramoorthy, Classes of meromorphic p-valent parabolic starlike functions with positive coefficients, Aust. J. Math. Anal. Appl. 2 (2005), 3.
  17. H. Silverman, Partial sums of starlike and convex functions, J. Math. Anal. Appl., 209 (1997), 221-227.
  18. B. A. Frasin and G. Murugusundaramoorthy, Partial sums of meromorphic multivalent functions with positive coefficients, Studia Univ. Babes-Balyai Math. Annul. (2005), 33-40.