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A Short Overview of Spiral-like Functions.

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Title: A Short Overview of Spiral-like Functions.
Authors: Dash, Debasmita1 lipsadash2018@gmail.com, Singh, Saumya2 saumya.singh@opju.ac.in, Samal, Debasmita3 debasmita.samal@opju.ac.in, Verma, Swati3 swati.verma@opju.ac.in, Singh, Abhishek Kumar4 sskitabhishek@gmail.com, Mishra, Manas Ranjan5 manas.mishra@opju.ac.in
Source: IAENG International Journal of Applied Mathematics. Jul2026, Vol. 56 Issue 7, p2589-2595. 7p.
Subjects: Analytic functions, Differential operators, Star-like functions, Convex functions, Taylor's series, Univalent functions
Abstract: This paper introduces a novel subclass of analytic and univalent functions constructed via the generalized Salagean operator In k. The class Mn(a,) = f S: R = ei I n+1 k f(z) I n k f(z) = > a, z generalizes well-known type functions, such as starlike, convex, and spiral-like functions. By analyzing the relation between I n+1 k and I n k, we derive sufficient conditions ensuring that a function belongs to the class Mn(a,). We also establish inequalities for the coefficients of the functions, which help to describe the behavior of the functions in terms of their Taylor series. These results bring together and extend previous work, offering a broader approach to studying analytic functions defined by generalized differential operators. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:This paper introduces a novel subclass of analytic and univalent functions constructed via the generalized Salagean operator In k. The class Mn(a,) = f S: R = ei I n+1 k f(z) I n k f(z) = > a, z generalizes well-known type functions, such as starlike, convex, and spiral-like functions. By analyzing the relation between I n+1 k and I n k, we derive sufficient conditions ensuring that a function belongs to the class Mn(a,). We also establish inequalities for the coefficients of the functions, which help to describe the behavior of the functions in terms of their Taylor series. These results bring together and extend previous work, offering a broader approach to studying analytic functions defined by generalized differential operators. [ABSTRACT FROM AUTHOR]
ISSN:19929978