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Abstract

The goal of this paper is to introduce a new subclass of meromorphic multivalent functions with higher derivatives inside a punctured open unit disk U*, by generalizing the Bessel function. The method used to derive the new findings on this topic is stated in section two of this paper. The product theorem between two functions and neighborhood properties was obtained using the recently discovered coefficient bounds for the new subclass. In addition, this paper attempted to address an important research gap in the subject of geometric function theory, which is the computational tools for coefficient bounds through the use of differential and integral operators and their generalizations, which led to knowing the behavior of the functions and comparing the results to know the best operator. Therefore, in this paper, after obtaining the coefficient bounds for the new subclass, the values of the coefficient bounds were calculated numerically, and an attempt was made to improve them using an integral operator. The numerical comparison of the two behaviors, which is mentioned in Table 1,, revealed that the integral operator used had a positive effect by providing the best bounds of the coefficient in comparison to the Bessel function, whereas the Bessel function had a negative effect on the function in this topic. Finally, based on the results in Table 1, it was concluded that the image of U* in the uv - plane is the set of all points that lie outside the open disk centered at (6,0) with radius 1, as shown in Fig. 1.

Keywords

Coefficient bounds, Hadamard product, Meromorphic functions, Multivalent functions, Neighborhood properties

Subject Area

Mathematics

Article Type

Article

First Page

2155

Last Page

2165

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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