Abstract
In this paper, we establish certain new subclasses of meromorphic harmonic functions using the principles of q-derivative operator. We obtain new criteria of sense preserving and univalency. We also address other important aspects, such as distortion limits, preservation of convolution, and convexity limitations. Additionally, with the help of sufficiency criteria, we estimate sharp bounds of the real parts of the ratios of meromorphic harmonic functions to their sequences of partial sums.
Highlights
1 Introduction and definitions Univalent harmonic functions are a new research area that was initially developed by Clunie and Sheil-Small [15]; see [40]
To understand the basics in a more clear way, we denote by H the family of harmonic functions f that can be represented in the series form 1∞ f (z) = h(z) + g(z) = +
The first paper in which a link was established between certain geometric nature of the analytic functions and the q-derivative operator is due to the authors [19]
Summary
Introduction and definitionsUnivalent harmonic functions are a new research area that was initially developed by Clunie and Sheil-Small [15]; see [40]. The authors of [24] contributed a certain family of harmonic closeto-convex functions involving the Alexander integral transform. (2021) 2021:471 and Murugusundaramoorthy [35, 36] analyzed the families of meromorphic harmonic function in D. To understand the basics in a more clear way, we denote by H the family of harmonic functions f that can be represented in the series form 1∞ f (z) = h(z) + g(z) = +
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