Geometric Features of a Multivalent Function Pertaining to Fractional Operators

Authors

  • K. Divya Priya Department of Mathematics, School of Advanced Science, Vellore Institute of Technology, Vellore, 632014, India
  • K. Thilagavathi Department of Mathematics, School of Advanced Science, Vellore Institute of Technology, Vellore, 632014, India https://orcid.org/0000-0002-1860-828X

DOI:

https://doi.org/10.37256/cm.5420245227

Keywords:

harmonic function, multivalent function, open unit disc, convolution, Prabhakar fractional operator

Abstract

The Prabhakar fractional operator is commonly acclaimed as the queen model of fractional calculus. The distinction between univalent and multivalent functions became more formalized as part of the broader field of geometric function theory. This area of mathematics focuses on the study of analytic functions with specific geometric properties, such as injectivity, and their applications in various domains, including conformal mapping and potential theory. This paper’s goal is to discover new results of the harmonic multivalent functions mceclip1-9e9533295b7404d69e7ab1032e429d17.png defined in the open unit disc mceclip2-59343eb1b5915bb97e12dbf1f02100b3.png. Let present mceclip3-aa3e314cd7e0c1fe0b7e66415af32c9d.png, the class of multivalent harmonic functions of the form mceclip1-9e9533295b7404d69e7ab1032e429d17.png in the open unit disc. Analyzing convolution with prabhahar fractional differential operator mceclip5.png with multivalent harmonic function to be in the class mceclip6.png. The coefficient inequality, growth rates, distortion properties, closure characteristics, neighborhood behaviors, and extreme points, all pertinent to this class mceclip7.png were explored.

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Published

2024-11-25

How to Cite

1.
K. Divya Priya, K. Thilagavathi. Geometric Features of a Multivalent Function Pertaining to Fractional Operators. Contemp. Math. [Internet]. 2024 Nov. 25 [cited 2024 Dec. 4];5(4):5434-53. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/5227

Issue

Section

Special Issue: Recent developments in pure and applied mathematics and its applications