Communications of the Korean Mathematical Society (대한수학회논문집)

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GEOMETRIC PROPERTIES ON (j, k)-SYMMETRIC FUNCTIONS RELATED TO STARLIKE AND CONVEX FUNCTION

  • Received : 2021.02.25
  • Accepted : 2021.04.15
  • Published : 2022.04.30
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Abstract

For j = 0, 1, 2,…, k - 1; k ≥ 2; and - 1 ≤ B < A ≤ 1, we have introduced the functions classes denoted by ST[j,k](A, B) and K[j,k](A, B), respectively, called the generalized (j, k)-symmetric starlike and convex functions. We first proved the sharp bounds on |f(z)| and |f'(z)|. Various radii related problems, such as radius of (j, k)-symmetric starlikeness, convexity, strongly starlikeness and parabolic starlikeness are determined. The quantity |a23 - a5|, which provide the initial bound on Zalcman functional is obtained for the functions in the family ST[j,k]. Furthermore, the sharp pre-Schwarzian norm is also established for the case when f is a member of K[j,k](α) for all 0 ≤ α < 1.

Keywords

Acknowledgement

The present work of the first author is supported by OSHEC, Government of Odisha, India. The second author acknowledges the support from INSPIRE Fellowship, DST, Government of India.

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