A Criterion for Bounded Functions

Abstract

Abstract. We consider a sufficient condition for w(z), analytic in |z| < 1, to be bounded in |z| < 1, where w(0) = w ′ (0) = 0. We apply it to the meromorphic starlike functions. Also, a certain Briot-Bouquet differential subordination is considered. Moreover, we prove that ifunder some additional assumptions on φ(z).

Notes on the Paper "A Criterion for Bounded Functions" [Bull. Korean Math. Soc. 53 (2016), No. 1, 215-225]

“…In [2] Nunokawa et al claimed that the above theorem is a new extension of a result by Hallenback and Ruscheweyh [1] because the function…”

“…Very recently, M. Nunokawa, S. Owa and J. Sokól published a paper [2] titled "A criterion for bounded functions" in Bull. Korean Math.…”

On Some Interesting Classes of Analytic Functions Related to Univalent Functions

“…Considering our next result, we need the following lemma due to Nunokawa, Owa, and Sokol [6]: Lemma 3. Let p(z) be analytic in U with p(0) = 1 and p(z) ̸ = 0 in U.…”