Value distribution for nth difference operator of meromorphic functions with maximal deficiency sum

  • Subhas S. Bhoosnurmath
  • Renukadevi S. Dyavanal
  • Mahesh Barki
  • Ashok Rathod
Original Research Paper


In this paper, we obtain the relationship between the characteristic function of meromorphic function having maximal deficiency sum and its higher order exact difference. We improve and generalise several results of Zhaojun Wu (Journal of Inequalities and Applications 530, [3]) to a great extent. We obtain an analogue of Shah and Singh (Mathematische Zeitschrift 65:171–174, [4]) in an improved form for \(\Delta _{c}f\). Also we establish a lower bound for \(K(\Delta _{c}f)=\limsup \limits _{r\rightarrow \infty }\frac{N\left( r,\Delta _{c}f\right) +N\left( r,\frac{1}{\Delta _{c}f}\right) }{T(r,\Delta _{c}f)}\). Under certain conditions we also show that \(K(\Delta _{c}^{n}f)=0\), for any integer \(n\ge 1\).


Nevanlinna theory Complex difference equations Meromorphic functions Maximal deficiency sum Small functions 

Mathematics Subject Classification




The first and third authors are supported by the SERB(DST) Project No. SB/S4/MS/842/2013, dated:10/12/2015. We are grateful to the referees for valuable suggestions and comments.

Compliance with ethical standards

Conflict of interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Human/animals participants

The authors declare that there is no research involving human participants and/or animals in the contained of this paper.


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Copyright information

© Forum D'Analystes, Chennai 2018

Authors and Affiliations

  • Subhas S. Bhoosnurmath
    • 1
  • Renukadevi S. Dyavanal
    • 1
  • Mahesh Barki
    • 1
  • Ashok Rathod
    • 1
  1. 1.Department of MathematicsKarnatak UniversityDharwadIndia

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