Certain Subclass of Meromorphic Functions with Positive Coefficients Defined by Bessel Function

Year 2020, Volume: 3 Issue: 3, 124 - 129, 29.09.2020

Santosh M. Popade Rajkumar N. Ingle P. Thırupathı Reddy B Venkateswarlu

https://doi.org/10.33434/cams.725158

Abstract

The aim of the present paper is to introduce a class $\Sigma _{p}^{ *}(G,H,\tau, c )$ of meromorphic univalent functions in $E=\{0<|z|<1\}$ and investigate coefficient estimates, distortion properties and radius of convexity estimates for this class. Furthermore, it is shown that this class is closed under convex linear combinations, convolutions and integral transforms.                                                                                                                                                                                                                                                                                                                                                         

Keywords

Convolutions, distortion, meromorphic

References

• [1] J. Clunie, On meromorphic schlicht functions, J. Londan Math. Soc., 34 (1959), 215-216 .
• [2] J. E. Miller, Convex meromorphic mapping and related functions, Proc. Amer. Math. Soc., 25 (1970), 220-228 .
• [3] Ch. Pommarenke, On meromorphic starlike functions, Pecific , J. Math., 13 (1963), 221-235 .
• [4] B.A. Uralegaddi and M. D. Ganigi, A certain class of meromorphic celly starlike functions with positive coefficients, Pure. Appl. Math. Sci., 26 ( 1987) , 75-81.
• [5] B. Venkateswarlu, P. Thirupathi Reddy, Ch. Meng and R. Madhuri Shilpa, A new subclass of meromorphic functions with positive coefficients defined by Bessel function, Note di Matematica (Accepted).
• [6] E. Deniz, H. Orhan and H.M. Srivastava, Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions, Taiwan J. Math., 15(2) (2011) , 883-917 .
• [7] G. N. Watson, A treatise on the theory of Bessel functions, 2nd edn. Cambridge University Press, Cambridge, (1994).
• [8] M. S. Robertson, Convolution of Schlicht functions, Proc. Amer. Math. Soc., 13 (1962), 585-587.
• [9] S. K. Bajpai, A note on a class of meromorphic univalent functions, Rev. Roumanie Math. Pure Appl., 22 (1997) , 295-297.