An application of Mittag-Leffler-type Poisson distribution on certain subclasses of analytic functions associated with conic domains

Heliyon. 2021 Oct 1;7(10):e08109. doi: 10.1016/j.heliyon.2021.e08109. eCollection 2021 Oct.

Abstract

In this paper our aim is to deduce some sufficient conditions and inclusion properties for Mittag-Leffler-type Poisson distribution series Ψ α , β m ( z ) = z + n = 2 Γ ( β ) m n - 1 Γ ( α ( n - 1 ) + β ) E α , β ( m ) z n to be in the classes k- ST [ A , B ] and k- UCV [ A , B ] of k-uniformly Janowski starlike and k-Janowski convex functions, respectively. Further, we obtain a condition for an integral operator G α , β m ( z ) = 0 z Φ α , β m ( t ) t d t to be in the class k- UCV [ A , B ] . Several corollaries and consequences of the main results are also considered.

Keywords: Convex functions; Hadamard product; Mittag–Leffler function; Starlike functions; Uniformly convex functions; Uniformly starlike functions.