On Certain Multivalent Functions

Abstract

Let𝒮*(p,α)be the class of functionsf(z)which are analytic andp-valently starlike of orderαin the open unit diskE. The object of the present paper is to derive an interesting condition forf(z)to be in the class𝒮*(p,α).

On the Starlikeness of Certain Class of Multivalent Analytic Functions

“…The proof of the following lemma is much akin to that of Theorem 1 which was obtained by Nunokawa et al [21] (see also Liu [22] and Yang [23]). We, therefore, choose to omit the analogous details involved.…”

On multivalent functions of bounded radius rotations

“…This result has been proved in [5]. (iii) For p = 1, it follows from Theorem 2.3 that f ∈ V k (α) is in R k (β 1 ), where β 1 is given by (2.7); see [8].…”

“…The results proved are sharp and improve some of the known results to a generalized form. We also solve completely an open problem posed by Nunokawa et al (2007) [5] as a special case of our main result. …”

A new criterion for multivalent starlike functions

“…In recent years, Nunokawa et al [2], Xu [3], Yang [4,5,6], Yang and Xu [7] and other authors obtained some criteria for multivalent starlikeness. In the present paper, we derive a new criterion for multivalent starlike functions by applying Jack's lemma.…”