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On the Zeros of the Differential Polynomials φ f l ( f ( k ) ) n − a

Author

Listed:
  • Jiantang Lu

    (School of Mathematics, Wuyi University, Jiangmen 529000, China)

  • Junfeng Xu

    (School of Mathematics, Wuyi University, Jiangmen 529000, China)

Abstract

Letting f be a transcendental meromorphic function, we consider the value distribution of the differential polynomials φ f l ( f ( k ) ) n − a , where φ ( ≢ 0 ) is a small function of f , l ( ≥ 2 ) , n ( ≥ 1 ) , k ( ≥ 1 ) are integers and a is a non-zero constant, and obtain an important inequality concerning the reduced counting function of φ f l ( f ( k ) ) n − a . Our results improve and generalize the results obtained by Xu and Ye, Karmakar and Sahoo, Chakraborty et.al, and Chen and Huang.

Suggested Citation

  • Jiantang Lu & Junfeng Xu, 2024. "On the Zeros of the Differential Polynomials φ f l ( f ( k ) ) n − a," Mathematics, MDPI, vol. 12(8), pages 1-13, April.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1196-:d:1376931
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