Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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A TURÁN-TYPE INEQUALITY FOR ENTIRE FUNCTIONS OF EXPONENTIAL TYPE

  • Received : 2021.11.16
  • Accepted : 2022.04.10
  • Published : 2022.06.30
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Abstract

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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Acknowledgement

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

References

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