Convolution properties for some subclasses of meromorphic p-valent functions of complex order associated with q-derivative

Document Type : Research Paper

Authors

Department of Mathematics, Payame Noor University, Tehran, Iran

Abstract

In this present investigation, for functions of the form $f(z) = 1/z^p + \sum^∞_{k=1−p} a_kz^k$, which are analytic in the punctured unit disk $U^∗ =\{z ∈ C : 0 < |z| < 1\}$, we introduce a new subclass of meromorphically p-valent functions and investigate convolution properties, Coefficient estimates and containment for this subclass.

Keywords

[1] M.K. Aouf, A.O. Mostafa, and H.M. Zayed, Convolution properties for some subclasses of meromorphic functions of complex order, Abstr. Appl. Anal. 2015 (2015), Article ID 973613, 1–6.
[2] M.K. Aouf and H.M. Srivastava, A new criterion for meromorphivally p-valent convex functions of order α, Math. Sci. Res. Hot. Line 8 (1997), no. 1, 7–12.
[3] G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990.
[4] S.B. Joshi and H.M. Srivastava, A certain family of meromorphivally multivalent functions, Comput. Math. Appl. 38 (1999), no. 3/4, 201–211.
[5] R. Kargar, A. Ebadian, and J. Sokol, Some properties of analytic tunctions related with bounded positive real part, Int. J. Nonlinear Anal. Appl. 8 (2017), 235–344.
[6] J.L. Liu and S. Owa, On a class of meromorphivally p-valent functions involving certain linear operators, Int. J. Math. Math. Sci. 32 (2002), 271–180.
[7] J.L. Liu and H.M. Srivastava, A linear operator and associated families of meromorphivally multivalent functions, J. Math. Anal. Appl. 259 (2001), 566–581.
[8] J.L. Liu and H.M. Srivastava, Some convolution conditions for starlikeness and convexity of meromorphivally multivalent functions, Appl. Math. Lett. 16 (2003), 13–16.
[9] S.S. Miller and P.T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J. 28 (1981), 157–171.
[10] A.O. Mostafa, M.k. Aouf, H.M. Zayed and T. Bulboaca, Convolution conditions for subelasse of mermorphic functions of complex order associated with basic Bessel functions, J. Egypt. Math. Soc. 25 (2017), 286–290.
[11] S.S. Miller and P.T. Mocanu, Differential Subordinations: Theory and Applications, Series on Monographs and Textbooks in Pure and Appl. Math. No.255 Marcel Dekker, Inc., New York, 2000.
[12] V. Ravichandran, S. Sivaprasadkumar, and K.G. Subramanian, Convolution conditions for spirallikeness and convex spirallikeness of certain mermorphic p-valent functions, J. Pure. Appl. Math. 11 (2004), 1–7.
[13] S. Ruscheweyh, Duality for Hadamaed products applications to extremal proplems for functions regular in the unit disc, Trans. Amer. Math. Soc. 210 (1975), 63–74.
[14] S. Ruscheweyh, Convolutions in Geometric Functions Theory, Les Presses De Montreal, Montreal, 1982.
[15] Z.-G. Wang and M.-L. Li, Some properties of certain family of multiplier transforms, Filomat 31 (2017), no. 1, 159–173.
Volume 15, Issue 9
September 2024
Pages 263-270
  • Receive Date: 20 March 2023
  • Revise Date: 12 August 2023
  • Accept Date: 28 August 2023