On Certain Properties of a Univalent Function Associated with Beta Function

Gegenbauer polynomials constitute a numerical tool that has attracted the interest of many function theorists in recent times mainly due to their real-life applications in many areas of the sciences and engineering. Their applications in geometric function theory (GFT) have also been considered by many researchers. In this paper, this powerful tool is associated with the prolific concepts of convolution and subordination. The main purpose of the research contained in this paper is to introduce and study a new subclass of analytic functions. This subclass is presented using an operator defined as the convolution of the generalized distribution and the error function and applying the principle of subordination. Investigations into this subclass are considered in connection to Carathéodory functions, the modified sigmoid function and Bell numbers to obtain coefficient estimates for the contained functions.

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Coefficient Results concerning a New Class of Functions Associated with Gegenbauer Polynomials and Convolution in Terms of Subordination

Olatunji

Oluwayemi

Oros

2023

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On Geometric Properties of a Certain Analytic Function with Negative Coefficients

2022

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Various function theorists have successfully defined and investigated different kinds of analytic functions. The applications of such functions have played significant roles in geometry function theory as a field of complex analysis. In this work, therefore, a certain subclass of univalent analytic functions of the form f(z)=z−∑m=2t[ω(2+β)+cγ−σ]Cm[mσ−cω(2+β)+cγ]Knzm−∑k=t+1∞akzk is defined using a generalized differential operator. Furthermore, some geometric properties for the class were established.

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On Certain Properties of a Univalent Function Associated with Beta Function

Cited by 2 publications

References 8 publications

Coefficient Results concerning a New Class of Functions Associated with Gegenbauer Polynomials and Convolution in Terms of Subordination

Coefficient Results concerning a New Class of Functions Associated with Gegenbauer Polynomials and Convolution in Terms of Subordination

On Geometric Properties of a Certain Analytic Function with Negative Coefficients

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