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http://dx.doi.org/10.4134/CKMS.c210322

ON FUNCTIONS STARLIKE WITH RESPECT TO n-PLY SYMMETRIC, CONJUGATE AND SYMMETRIC CONJUGATE POINTS  

Malik, Somya (Department of Mathematics National Institute of Technology)
Ravichandran, Vaithiyanathan (Department of Mathematics National Institute of Technology)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.4, 2022 , pp. 1025-1039 More about this Journal
Abstract
For given non-negative real numbers 𝛼k with ∑mk=1 𝛼k = 1 and normalized analytic functions fk, k = 1, …, m, defined on the open unit disc, let the functions F and Fn be defined by F(z) := ∑mk=1 𝛼kfk(z), and Fn(z) := n-1 ∑n-1j=0 e-2j𝜋i/nF(e2j𝜋i/nz). This paper studies the functions fk satisfying the subordination zf'k(z)/Fn(z) ≺ h(z), where the function h is a convex univalent function with positive real part. We also consider the analogues of the classes of starlike functions with respect to symmetric, conjugate, and symmetric conjugate points. Inclusion and convolution results are proved for these and related classes. Our classes generalize several well-known classes and the connections with the previous works are indicated.
Keywords
Starlike functions; convex functions; symmetric points; conjugate points; convolution;
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