Zeros and value sharing results for
q-shifts difference and differential
polynomials

Raj Shree Dhar

doi:https://doi.org/10.14445/22315373/IJMTT-V65I11P507

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 11 | Year 2019 | Article Id. IJMTT-V65I11P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I11P507

Zeros and value sharing results for q-shifts difference and differential polynomials

Raj Shree Dhar

Abstract

In this paper, we consider the zero distributions of q-shift monomials and difference polynomials of meromorphic functions with zero order, that extends the classical Hayman results on the zeros of differential polynomials to q-shift difference polynomials. We also investigate problem of q-shift difference polynomials that share a common value.

Keywords

Entire and Meromorphic function; q-shift; q-difference polynomial; shared values; Nevanlinna theory.

References

[1] Hayman, W.K.: Meromorphic functions- Clarenden Press, Oxford, 1964.
[2] Yi, H.X., Yang, C.C.: Uniqueness Theory of Meromorphic Functions- Kluwer Academic, Dordrecht (2003).[Chinese original: Science Press, Beijing (1995)].
[3] Hayman, W.K.: Picard values of meromorphic functions and their derivatives- Ann. of Math. (2), 70 (1959), pp.9-42.
[4] Mues E, ber ein: Problem von Hayman- Math. Z. 164 (1979), pp.239-259.
[5] Bergweiler, W. and Eremenko, A.: On the singularities of the inverse to a meromorphic function of fnite order- Revista Matemtica Iberoamericana, 11 (1995), pp.355-373.
[6] Laine, I., Yang, C.C.: Value distribution and uniqueness of difference polynomials -Proc. Japan Acad. Ser. A, 83(2007), pp.148-151.
[7] Zhang, J. and Korhonen,R.: On the Nevanlinna characteristic of f(qz) and its applications- Journal of Mathematical Anal. and Appl., vol. 369, no. 2, 2010, pp.537-544.
[8] Barnett,D., Halburd,R.J., Korhonen, Morgan: Applications of Nevanlinna theory to q-difference equations- Proc. Roy. Soc. Edinburgh Sect. A 137(2007),pp.457-474.
[9] Liu, K., Liu, X., Cao, T.B. : Value distribution of the difference opera-tor, Advances in Difference equations, Vol.2011, Art ID 234215,12 pages.
[10] W. Bergweiler, K. Ishizaki, N. Yanagihara, Meromorphic solutions of some functional equations, Methods Appl. Anal. 5 (1998), pp.248-258, correction:Methods Appl. Anal. 6 (1999).
[11] Yang, C.C., Hua, X.H.: Uniqueness and value sharing of meromorphic functions, Ann. Acad.Sci. Fenn. Math. 22(1997), pp.395-406.
[12] Doeringer, W.: Exceptional values of Differential Polynomials, Pacific J. of Math., 98(no. 1) 1982, pp.55-62.

Citation :

Raj Shree Dhar, "Zeros and value sharing results for q-shifts difference and differential polynomials," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 11, pp. 62-71, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I11P507