Abstract
This study defines a new linear differential operator via the Hadamard product between a q-hypergeometric function and Mittag–Leffler function. The application of the linear differential operator generates a new subclass of meromorphic function. Additionally, the study explores various properties and features, such as convex properties, distortion, growth, coefficient inequality and radii of starlikeness. Finally, the work discusses closure theorems and extreme points.
Highlights
Let Σ denote the class of functions of the form f ( z ) = z −1 + ∞ ∑ aj zj, (1)j =1 which are analytic in the punctured open unit disk U∗ = {z : z ∈ C, 0 < |z| < 1} = U/{0}.Let Σ∗ (ρ) and Σk (ρ) denote the subclasses of Σ that are meromorphically starlike functions of order ρ and meromorphically convex functions of order ρ respectively
In most of our work related to Mittag–Leffler functions, we study the geometric properties, such as the convexity, close-to-convexity and starlikeness
Studying the theory of analytical functions has been an area of concern for many researchers
Summary
One example that can be associated with the hypergeometric functions is the well-known Dziok–Srivastava operator [5,6] defined via the Hadamard product. A range of meromorphic function subclasses have been explored by, for example, Challab et al [26], Elrifai et al [27], Lashin [28], Liu and Srivastava [22] and others These works have m ( a , b , λ; D, H, d ) of Σ, which involves the operator inspired our introduction of the new subclass Tα,β l r [.
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