Certain geometric properties of the Wright function

Abstract

In this work, the Wright function with their normalizations are considered. Several conditions are obtained so that the Wright function has certain geometric properties including univalency, starlikeness, convexity and close-to-convexity in the open unit disk. Results obtained are new and their usefulness are depicted by deducing several interesting corollaries and relevance with some of the earlier results are also pointed out.

Geometric Properties of Normalized Wright Functions

“…By taking α " 0 in Corollary 2.5, we obtain the following corollary. [23], (p. 206, Theorem 2.7 (a), (c))).…”

“…On this subject, there are many works such as [11][12][13]17]. In [23], Prajapat investigated some geometric properties such as starlikeness and convexity of the normalized Wright functions Φ p1q pλ, µ; zq and Φ p2q pλ, µ; zq. Investigating geometric properties of the normalized Wright functions Φ p1q pλ, µ; zq and Φ p2q pλ, µ; zq in a class more generalized than the class of starlike and convex functions is also a research interest.…”

Univalence of certain integral operators involving normalized wright functions

“…Note that, recently the function G p ; : U ! C de…ned by (3.8) was investigated by Prajapat [11] and he obtained some su¢ cient conditions for the univalence this function. Now, on the univalence of the integral operator p…”

Corrigendum to ‘Certain geometric properties of the Wright function’

“…30C45; 33C20; 46F12 Theorem 2.13 in [1] cannot be in its current form. The main result and the proof of Theorem 2.13 should be as follows.…”