| Summary: | We denote by A the class of all univalent and analytic functions f(z)=z+?k=28akzk in the open unit disk ??={z: |z|<1}. Here, the classes with respect to all functions in A that are univalent in ?? are further represented by S. There is an inverse f-1 for each function f?S. If both f and its inverse g=f-1 are univalent, then, a function f?A is called bi-univalent in ??. Results for covering theorem, distortion theorem, rotation theorem, growth theorem, as well as the convexity radius with respect to the functions of the class ? of bi-univalent functions that are connected to a generalised differential operator D?,as,m,kf(z), are obtained in this paper. In order to get the desired results, we utilised the elementary transformations where the class ? is preserved. Subsequently, the theorems of the required properties of bi-univalent functions are attained. These results can be reduced to other previous well-known findings by assigning different initial coefficient |a2|. © 2024 Author(s).
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