Geodesic
Uniqueness results for the difference operators using the conception of sharing value
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2024), pp. 85-105 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this article we considered a difference-differential polynomial of a transcendental entire function and established in the first two theorems criteria for infinitely many solutions for such type of equation. In the 3rd and 4th theorems we introduced $k$-th order differentiation of a polynomial of a transcendental entire function and its difference operator, and developed some uniqueness results in different aspects using the conception of sharing value. We elaborated our results with some remarks and analysed the results in different aspects and conditions. The results generalize and improve previous results of Zhang–Lin and Benerjee–Majumder. We introduced some notes to draw the gravity of improvement and generalisation of the previous results.
Keywords: difference operator, sharing value, transcendental entire function, uniqueness. 
@article{IVM_2024_7_a7,
     author = {A. Shaw},
     title = {Uniqueness results for the difference operators using the conception of sharing value},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {85--105},
     year = {2024},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2024_7_a7/}
}
TY  - JOUR
AU  - A. Shaw
TI  - Uniqueness results for the difference operators using the conception of sharing value
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2024
SP  - 85
EP  - 105
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/IVM_2024_7_a7/
LA  - ru
ID  - IVM_2024_7_a7
ER  - 
%0 Journal Article
%A A. Shaw
%T Uniqueness results for the difference operators using the conception of sharing value
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2024
%P 85-105
%N 7
%U http://geodesic.mathdoc.fr/item/IVM_2024_7_a7/
%G ru
%F IVM_2024_7_a7
A. Shaw. Uniqueness results for the difference operators using the conception of sharing value. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2024), pp. 85-105. http://geodesic.mathdoc.fr/item/IVM_2024_7_a7/

[1] Hayman W.K., Meromorphic functions, Oxford Mathematical Monographs Clarendon Press, Oxford, 1964 | MR | Zbl

[2] Yang L., Value distribution theory, Springer-Verlag; Sci. Press, 1993 | MR | Zbl

[3] Yi H.X., Yang C.C., Uniqueness theory of meromorphic functions, Sci. Press, Beijing, 1995

[4] Lahiri I., “Value distribution of certain differential polynomials”, Int. J. Math. Math. Sci., 28 (2001), 83–91 | DOI | MR | Zbl

[5] Lahiri I., “Weighted value sharing and uniqueness of meromorphic functions”, Complex Var. Theory Appl., 46 (2001), 241–253 | MR | Zbl

[6] Zhang X.Y., Lin W.C., “Uniqueness and value-sharing of entire functions”, J. Math. Anal. Appl., 343 (2008), 938–950 | DOI | MR | Zbl

[7] Banerjee A., Majumder S., “Uniqueness of certain type of differential-difference and difference polynomials”, Tamkang J. Math., 49:1 (2018), 1–24 | DOI | MR | Zbl

[8] Yang C.C., “On deficiencies of differential polynomials. II”, Math. Z., 125 (1972), 107–112 | DOI | MR | Zbl

[9] Zhang J.L., Yang L.Z., “Some results related to a conjecture of R. Brück”, J. Inequal. Pure Appl. Math., 8 (2007), 18 | MR

[10] Chiang Y.M., Feng S.J., “On the Nevanlinna characteristic $f(z+\eta)$ and difference equations in complex plane”, Ramanujan J., 16 (2008), 105–129 | DOI | MR | Zbl