Abstract
The main purpose of this article is to introduce the new subclass of analytic functions whose coefficients are Borel distributions in the Janowski domain. Further, we investigate some useful number of properties such as Fekete–Szegő inequality, necessary and sufficient condition, growth and distortion approximations, convex linear combination, arithmetic mean, radii of close-to-convexity and starlikeness and partial sums, followed by some extremal functions for this defined class. The symmetry properties and other properties of the subclass of functions introduced in this paper can be studied as future research directions.
Highlights
Introduction and MotivationLet A0 represent the collections of analytic functions f inside open unit disc D = {ξ ∈ C : |ξ| < 1} with normalized form ∞f (ξ) = ξ + ∑ anξn, ξ ∈ D. (1) n=2as indicated by S, a subclass of A0 consists of all functions that are univalent inside open unit disc D
Motivated from all the above discussions and work from Khan et al [16], in which they introduced a class of analytic functions with Mittag–Leffler type Poisson distribution in the Janowski domain, analytic functions with Mittag–Leffler type Borel distribution [17], and the work in the articles [18,19], we introduce a new class of analytic functions with the help of operator (2), as follows: SB∗ (A, B) =
We evaluate Fekete–Szegö inequality, necessary and sufficient conditions, growth and distortion bounds, radii of starlikeness and convexity, radii of close-to-convexity and partial sums results for the newly defined class
Summary
If the function g is univalent in D, it follows that: f (ξ) ≺ g(ξ) (ξ ∈ D) ⇒ f (0) = g(0) and f (D) ⊂ g(D). We evaluate Fekete–Szegö inequality, necessary and sufficient conditions, growth and distortion bounds, radii of starlikeness and convexity, radii of close-to-convexity and partial sums results for the newly defined class. Let f ∈ A0 be assigned to the class SB∗ (A, B).
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