Convolution properties for subclasses of meromorphic univalent functions of complex order

Abstract

Using the new linear operatorwhere l > 0, λ ≥ 0, and m ∈ N0 = N ∪ {0}, we introduce two subclasses of meromorphic analytic functions, and we investigate several convolution properties, coefficient inequalities, and inclusion relations for these classes.

CONVOLUTION CONDITIONS FOR CERTAIN SUBCLASSES OF MEROMORPHIC p-VALENT FUNCTIONS

“…(iii) Taking p = 1, q → 1 − and λ = 0 in Theorem 2.1 and 2.2, our results matches with Aouf [3] and Bulboacȃ et al . [4]. (iv) Taking p = 1 in Theorem 2.1 and 2.2 our results matches with Mostafa et al .…”

Applications of the differential operator to a class of meromorphic univalent functions

“…Several differential and integral operators were introduced and studied, see for example [1,3,16,21,22,25,27]. For the recent work on linear operators for meromorphic functions, we refer to [4,6,10,11]. In this work we consider the operator defined by El-Ashwah [10] and El-Ashwah and Aouf [11,12].…”

Starlike functions associated with $ \tanh z $ and Bernardi integral operator

“…If h(z) = z/(1 − z), then g * h = g and if h(z) = z/(1 − z) 2 , then g * h = zg for all f ∈ A [11]. The convolution properties for various subclasses have discussed in [8,13]. For the function f ∈ A, the q th Hermitian-Toeplitz determinant is given by HT q (n) := [a ij ], where a ij = a n+j−i for j ≥ i and a ij = a ji for j < i.…”