On multivalent functions of bounded radius rotations

Abstract

a b s t r a c tIn this work, we consider the classes of p-valent analytic functions with bounded radius and bounded boundary rotations. 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.

Hankel determinant problem of a subclass of analytic functions

“…This class was introduced and studied in details by Moulis [1]. For l = 0, we obtain the class V k (σ ) of analytic functions with bounded boundary rotations of order s studied by Padmanabhan et al [2] and when s = 0 and l = 0, we get the class V k discussed by Paatero [3], see also [4][5][6][7][8]. Also it can easily be shown that…”

Binomial Series-Confluent Hypergeometric Distribution and Its Applications on Subclasses of Multivalent Functions

“…This paperâe™s novel findings are motivated by the excellent outcomes lately achieved through the integral and derivative operators in the field of geometric function theory. Our inspiration to further investigate the binomial series-confluent hypergeometric distribution was sparked by reading about the applications of an operator on new subclasses of univalent functions and how they relate to classical theories of differential subordination and superordination [15,16,[29][30][31][32][33] and the references cited therein. This led us to consider the idea of introducing and studying new subclasses of univalent functions in ∆ with bounded boundary rotation.…”

“…,n,ϑ,υ,m κ,p,j (℘) and K ,n,ϑ,υ,m κ,p,j (η, ℘), motivated by the earlier studies on bounded boundary rotations and differential subordination [3,11,24,30,31,33,34] and using following Lemmas 1-3, we discuss inclusion properties involving the differential operator D…”