Some Properties of a Generalized Class of Analytic Functions Related with Janowski Functions

Abstract

We define a class T k A, B, α, ρ of analytic functions by using Janowski's functions which generalizes a number of classes studied earlier such as the class of strongly close-to-convex functions. Some properties of this class, including arc length, coefficient problems, and a distortion result, are investigated. We also discuss the growth of Hankel determinant problem.

Upper Bound of Second Hankel Determinant for Certain Subclasses of Analytic Functions

“…The growth rate of Hankel determinant ( ) as → ∞ was investigated, respectively, when is a member of certain subclass of analytic functions, such as the class of p-valent functions [7,8], the class of starlike functions [7], the class of univalent functions [9], the class of close-to-convex functions [10], the class of strong close-to-convex functions [11], a new class [12], and a new class̃( , , ) [13]. Similar to the above discussions, we can also refer to [14,15]. Ehrenborg [16] studied the Hankel determinant of exponential polynomials.…”

Properties of Certain Classes of Holomorphic Functions Related to Strongly Janowski Type Function

“…Let S denote the subclass of A of univalent functions in ∇ and C, S * , and K represent the usual subclasses of S that are convex, star-like, and close to convex in ∇, respectively. A number of classes related with strongly star-like and strongly convex functions have been studied; for details, see [1][2][3][4][5][6].…”

“…)), which is the result for the well-known class P of Caratheodory functions Lemma 6 (see [17]). Let g(z) ∈ A be of form (1). en, g(z) ∈ V m (ϱ), where m ≥ 2 and 0 ≤ ϱ < 1 if and only if (i) ere exists some…”

A New Class of Analytic Functions Associated with Sălăgean Operator

“…Later on, Kuroki and Owa [3] discussed the fact that the condition | | ≤ 1 can be omitted from the conditions in part ( ) of (7). Janowski functions are being studied and extended in different directions by several renowned mathematicians like Noor and Arif [4], Arif et al [5], Polatog lu [6], Cho [7], Cho et al [8,9], Liu and Noor [10], Liu and Patel [11], Liu and Srivastava [12,13], etc. For a function of the form (1) and = 1, 2, 3 .…”