On certain meromorphic p-valent starlike functions

DIFFERENTIAL SUBORDINATIONS AND SUPERORDINATIONS OF CERTAIN MEROMORPHIC FUNCTIONS ASSOCIATED WITH AN INTEGRAL OPERATOR Vol. 2(1) Jan 2014, No. 15, pp. 172-183 H. E. DARWISH, A. Y. LASHIN AND S. M. SOILEH

“…Proof. Let p(z) defined by (9) and ψ(z) defined by (14). Since φ ∈ Φ ′ H [Ω, q], from ( 14) and (29) we have 13), we see that the admissibility condition for φ ∈ Φ ′ H [Ω, q] is equivalent to the admissibility condition for ψ as given in Definition 2.…”

“…A similar problem for analytic functions was studied by Aghalary et al [1], Ali et al [3], Aouf [4], Aouf et al [5], Aouf and Seoudy [6], kim and Srivastava [8], and Raina and Sharma [15]. Also Ali et al [2], Liu and Owa [10], and Kamali [14] investigated a subordination problem for meromrphic functions. Additionally, the corresponding superordination problem is investigated, and several Differential Sandwich-type results are obtained.…”

DIFFERENTIAL SUBORDINATIONS AND SUPERORDINATIONS OF CERTAIN MEROMORPHIC FUNCTIONS ASSOCIATED WITH A FAMILIY OF MULTIPLIER TRANSFORMATIONS Vol. 2(2) July 2014, No. 18, pp. 178-188. H. E. DARWISH, A. Y. LASHIN, AND B. H. RIZQAN

“…A similar problem for analytic functions was studied by Aghalary et al [1], Ali et al [3], Aouf [4], Aouf et al [5], Aouf and Seoudy [6], and Kim and Srivastava [14]. Also Ali et al [2], Liu and Owa [15] and Kamali [13] investigated a subordination problem for meromorphic functions. Additionally, the corresponding superordination problem is investigated, and several differential sandwich-type results are obtained.…”

On coefficients of some p-valent starlike functions

“…A function f analytic in a domain D ∈ C is called p-valent in D, if for every complex number w, the equation f (z) = w has at most p roots in D, so that there exists a complex number w 0 such that the equation f (z) = w 0 has exactly p roots in D. The properties of multivalent functions under several operators were established recently in several papers, see for instance [3,6,8,16]. Meromorphic multivalent functions was considered recently in [4,5,9]. Denote by A p , p ∈ N = {1, 2, .…”