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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]
Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 195026891
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  Data: A Short Overview of Spiral-like Functions.
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  Data: <searchLink fieldCode="AR" term="%22Dash%2C+Debasmita%22">Dash, Debasmita</searchLink><relatesTo>1</relatesTo><i> lipsadash2018@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Singh%2C+Saumya%22">Singh, Saumya</searchLink><relatesTo>2</relatesTo><i> saumya.singh@opju.ac.in</i><br /><searchLink fieldCode="AR" term="%22Samal%2C+Debasmita%22">Samal, Debasmita</searchLink><relatesTo>3</relatesTo><i> debasmita.samal@opju.ac.in</i><br /><searchLink fieldCode="AR" term="%22Verma%2C+Swati%22">Verma, Swati</searchLink><relatesTo>3</relatesTo><i> swati.verma@opju.ac.in</i><br /><searchLink fieldCode="AR" term="%22Singh%2C+Abhishek+Kumar%22">Singh, Abhishek Kumar</searchLink><relatesTo>4</relatesTo><i> sskitabhishek@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Mishra%2C+Manas+Ranjan%22">Mishra, Manas Ranjan</searchLink><relatesTo>5</relatesTo><i> manas.mishra@opju.ac.in</i>
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  Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Jul2026, Vol. 56 Issue 7, p2589-2595. 7p.
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  Data: <searchLink fieldCode="DE" term="%22Analytic+functions%22">Analytic functions</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+operators%22">Differential operators</searchLink><br /><searchLink fieldCode="DE" term="%22Star-like+functions%22">Star-like functions</searchLink><br /><searchLink fieldCode="DE" term="%22Convex+functions%22">Convex functions</searchLink><br /><searchLink fieldCode="DE" term="%22Taylor's+series%22">Taylor's series</searchLink><br /><searchLink fieldCode="DE" term="%22Univalent+functions%22">Univalent functions</searchLink>
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  Label: Abstract
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  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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        PageCount: 7
        StartPage: 2589
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      – SubjectFull: Analytic functions
        Type: general
      – SubjectFull: Differential operators
        Type: general
      – SubjectFull: Star-like functions
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      – SubjectFull: Convex functions
        Type: general
      – SubjectFull: Taylor's series
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      – SubjectFull: Univalent functions
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              M: 07
              Text: Jul2026
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              Y: 2026
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