Shift Differential-Difference Polynomials of Meromorphic Functions and Their Uniqueness Concerning Weighted Sharing

Jayanta Roy; Dilip Chandra Pramanik

doi:10.5644/SJM.22.01.06

Authors

Jayanta Roy Center for Distance and online education, University of North Bengal, Raja Rammohunpur, Darjeeling-734013, West Bengal ,India
Dilip Chandra Pramanik Department of Mathematics, University of North Bengal, Raja Rammohunpur, Darjeeling-734013, West Bengal, India

DOI:

https://doi.org/10.5644/SJM.22.01.06

Keywords:

Meromorphic function, Differential polynomial, Weighted sharing

Abstract

The purpose of the paper is to study the uniqueness problems of certain types of shift differential-difference polynomials of meromorphic functions sharing a small function under the notion of relaxed weighted sharing.

Statistics

Abstract: 0 / PDF: 0

References

A. Banerjee, Meromorphic functions sharing one value, Int. J. Math. Sci., 22 (2005), 3587–3598.

A. Banerjee and S. Majumder, On the uniqueness of a power of a meromorphic function sharing a small function with the power of its derivative, Comment. Math. Univ. Carolin., 51(4) (2010), 565–576.

A. Banerjee and B. Chakraborty, Further investigations on a questions of Zhang and Lu, Ann. Univ. Paedagog. Crac. Stud. Math., 14 (2015), 105–119.

M. R. Chen and Z. X. Chen, Properties of difference polynomials of entire functions with finite order, Chinese Ann. Math., 33A (2012), 359–374.

Y. M. Chiang and S. J. Feng, On the Nevanlinna characteristic of $f(z+eta)$ and difference equations in the complex plane, Ramanujan J., 16(1) (2008), 105–129.

W. K. Hayman, Meromorphic function, Clarendon Press, Oxford, 1964.

I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46 (2001), 241–253.

I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161 (2001), 193–206.

I. Laine and C. C. Yang, Value distribution of difference polynomials, Proc. Japan Acad. Ser. A, 83 (2007), 148–151.

K. Liu and L. Z. Yang, Value distribution of the difference operator, Arch. Math., 92 (2009), 270–278.

F. H. Liu and H. X. Yi, Uniqueness of meromorphic functions concerning the difference polynomials, Kyungpook Math. J., 55 (2015), 411–427.

X. Luo and W. C. Lin, Value sharing results for shifts of meromorphic functions, J. Math. Anal. Appl., 377 (2011), 441–449.

H. P. Waghamore, Generalization of value distribution and uniqueness of certain types of difference polynomials, Tbilisi Mathematical Journal, 11(1) (2018), 1–13.

L. Yang, Value distributions theory, Springer-Verlag, Berlin, 1993.

H. X. Yi and C. C. Yang, Uniqueness theory of meromorphic functions (in Chinese), Science Press, Beijing, 1995.

K. Zhang and H. X. Yi, The value distribution and uniqueness of one certain type of differential-difference polynomials, Acta Mathematica Scientia Series Manuscript, 34(3) (2014), 719–728.

J. L. Zhang and L. Z. Yang, Some results related to a conjecture of R. Bruck, J. Inequal. Pure Appl. Math., 8 (2007), Art. 18.

J. L. Zhang, Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl., 367 (2010), 401–408.