Convolutions of Harmonic Mappings Convex in the Horizontal Direction

In the present exploration, the authors define and inspect a new class of functions that are regular in the unit disc D ≔ ς ∈ ℂ : ς < 1 , by using an adapted version of the interesting analytic formula offered by Robertson (unexploited) for starlike functions with respect to a boundary point by subordinating to an exponential function. Examples of some new subclasses are presented. Initial coefficient estimates are specified, and the familiar Fekete-Szegö inequality is obtained. Differential subordinations concerning these newly demarcated subclasses are also established.

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On a Subclass of Analytic Functions That Are Starlike with Respect to a Boundary Point Involving Exponential Function

Lecko

Murugusundaramoorthy

Sivasubramanian³

2022

Journal of Function Spaces

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Convolutions of Harmonic Mappings Convex in the Horizontal Direction

Abstract: In this paper, we establish some results concerning the convolutions of harmonic mappings convex in the horizontal direction with harmonic vertical strip mappings. Furthermore, we provide examples illustrated graphically with the help of Maple to illuminate the results.

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References 19 publications

On a Subclass of Analytic Functions That Are Starlike with Respect to a Boundary Point Involving Exponential Function

On a Subclass of Analytic Functions That Are Starlike with Respect to a Boundary Point Involving Exponential Function

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