Korean Journal of Mathematics

  • 제30권2호
  • /
  • Pages.199-203
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  • 2022
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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A TURÁN-TYPE INEQUALITY FOR ENTIRE FUNCTIONS OF EXPONENTIAL TYPE

  • 투고 : 2021.11.16
  • 심사 : 2022.04.10
  • 발행 : 2022.06.30
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초록

Let f(z) be an entire function of exponential type τ such that ║f║ = 1. Also suppose, in addition, that f(z) ≠ 0 for ℑz > 0 and that $h_f(\frac{\pi}{2})=0$. Then, it was proved by Gardner and Govil [Proc. Amer. Math. Soc., 123(1995), 2757-2761] that for y = ℑz ≤ 0 $${\parallel}D_{\zeta}[f]{\parallel}{\leq}\frac{\tau}{2}({\mid}{\zeta}{\mid}+1)$$, where Dζ[f] is referred to as polar derivative of entire function f(z) with respect to ζ. In this paper, we prove an inequality in the opposite direction and thereby obtain some known inequalities concerning polynomials and entire functions of exponential type.

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과제정보

The authors are highly grateful to the referee for his/her useful suggestions.

참고문헌

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  3. R. B. Gardner and N. K. Govil, Some inequalities for entire functions of exponential type, Proc. Amer. Math. Soc., 123 (9) (1995), 2757-2761. https://doi.org/10.1090/S0002-9939-1995-1257107-7
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