Some subclasses of multivalent functions involving a certain linear operator

Abstract

The authors investigate various inclusion and other properties of several subclasses of the class A p of normalized p-valent analytic functions in the open unit disk, which are defined here by means of a certain linear operator. Problems involving generalized neighborhoods of analytic functions in the class A p are investigated. Finally, some applications of fractional calculus operators are considered.  2005 Elsevier Inc. All rights reserved.

Certain Subclasses of Multivalent Functions Defined by New Multiplier Transformations

“…The bound in (49) is sharp with the extremal function given by (50). The proof of the theorem is thus complete.…”

“…We follow earlier investigations (based upon the familiar concept of neighborhoods of analytic functions) by Goodman [21], Ruscheweyh [40] and others including Srivastava et al [50,53], Orhan [33,34], Deniz et al [17], and Aouf et al [8] (see also [11]). First, we define the (n, η)-neighborhood of function f (z) ∈ A(n, p) of the form (1) by means of Definition 4.1 below.…”

“…Various operators of fractional calculus (that is, fractional integrals and fractional derivatives) have been studied in the literature extensively (cf., e.g., [37,50,54]; see also [14,51,52] and the various references cited therein). In our present investigation, we recall the following definitions.…”

On subclass of meromorphic multivalent functions associated with Liu-Srivastava operator

“…The Liu-Srivastava operator is studied in [1,13,16], is the meromorphic analogue of the DziokSrivastava [3] linear operator. Special cases of the Liu-Srivastava linear operator include the meromorphic analogue of the Carlson-Shaffer linear operator L p (a, c) = H p,2,1 (1, a, c) studied among others by Liu and Srivastava [7], Liu [6] and Yang [20].…”

Differential Sandwich Theorem for Multivalent Meromorphic Functions associated with the Liu-Srivastava Operator

“…It is clear that the Liu-Srivastava operator investigated in [11,22,23] is the meromorphic analogue of the DziokSrivastava [12] linear operator.…”