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ZERO DISTRIBUTION OF SOME DELAY-DIFFERENTIAL POLYNOMIALS

  • Laine, Ilpo;Latreuch, Zinelaabidine
    • 대한수학회보
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    • 제57권6호
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    • pp.1541-1565
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    • 2020

  • Let f be a meromorphic function of finite order ρ with few poles in the sense Sλ(r, f) := O(rλ+ε) + S(r, f), where λ < ρ and ε ∈ (0, ρ - λ), and let g(f) := Σkj=1bj(z)f(kj)(z + cj) be a linear delay-differential polynomial of f with small meromorphic coefficients bj in the sense Sλ(r, f). The zero distribution of fn(g(f))s - b0 is considered in this paper, where b0 is a small function in the sense Sλ(r, f).

  • https://doi.org/10.4134/BKMS.b200051 인용 PDF KSCI

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

  • Gochhayat, Priyabrat;Prajapati, Anuja
    • 대한수학회논문집
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    • 제37권2호
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    • pp.455-472
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    • 2022

  • 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.

  • https://doi.org/10.4134/CKMS.c210072 인용 PDF KSCI