Fractal and Fractional (Feb 2024)

Properties of a Class of Analytic Functions Influenced by Multiplicative Calculus

  • Kadhavoor R. Karthikeyan,
  • Gangadharan Murugusundaramoorthy

DOI
https://doi.org/10.3390/fractalfract8030131
Journal volume & issue
Vol. 8, no. 3
p. 131

Abstract

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Motivated by the notion of multiplicative calculus, more precisely multiplicative derivatives, we used the concept of subordination to create a new class of starlike functions. Because we attempted to operate within the existing framework of the design of analytic functions, a number of restrictions, which are in fact strong constraints, have been placed. We redefined our new class of functions using the three-parameter Mittag–Leffler function (Srivastava–Tomovski generalization of the Mittag–Leffler function), in order to increase the study’s adaptability. Coefficient estimates and their Fekete-Szegő inequalities are our main results. We have included a couple of examples to show the closure and inclusion properties of our defined class. Further, interesting bounds of logarithmic coefficients and their corresponding Fekete–Szegő functionals have also been obtained.

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