In this paper, we consider the boundedness of the Libera operator on Dirichlet spaces in terms of the Schur test. Moreover, we get its point spectrum and norm.

in this paper, we consider the boundedness of the libera operator on dirichlet spaces in terms of the schur test. moreover, we get its point spectrum and norm.

In this paper we prove a starlikeness property for the Bernardi operator concerning ( ) α S -class and two particular properties for Libera and Alexander operators.

We consider the space B logα , of analytic functions on the unit disk D, defined by the requirement ∫ D |f (z)|φ(|z|) dA(z) < ∞, where φ(r) = log(1/(1 − r)) and show that it is a predual of the “log-Bloch” space and the dual of the corresponding little Bloch space. We prove that a function f(z) = ∑ ∞ n=0 anz with an ↓ 0 is in B1logα iff ∑ ∞ n=0 log(n+2)/(n+1) < ∞ and apply this to obtain a crit...

The research presented in this paper deals with analytic p-valent functions related to the generalized probability distribution open unit disk U. Using Hadamard product or convolution, function fs(z) is defined as involving an and expressed terms of functions. Neighborhood properties for are established. Further, by applying a previously introduced linear transformation using extended Libera in...

In this paper, we introduce a new class of p-valent harmonic functions defined by an integral operator. Coefficient inequalities, distortion bounds for the functions belonging to this class are obtained. The invariance of the class Hp(n, α) under convolution, convex linear combination and also under generalized Bernardi-Libera Livingston integral operator are discussed. 2000 Mathematics Subject...

Using the principle of subordination, we obtain some inclusion properties of subclasses of p-valent functions defined by multiplier transformation. Also inclusion properties of classes involving the generalized Libera integral operator are obtained. 2000 Mathematics Subject Classification: 30C45.