Zeros and Weighted value sharing of q-shift difference-differential polynomials of entire and meromorphic functions
B. N., N., Waghamore, H. (2024). Zeros and Weighted value sharing of q-shift difference-differential polynomials of entire and meromorphic functions. EKB Journal Management System, 15(1), 1-20. doi: 10.21608/jfca.2023.207861.1016
NaveenKumar B. N.; Harina P Waghamore. "Zeros and Weighted value sharing of q-shift difference-differential polynomials of entire and meromorphic functions". EKB Journal Management System, 15, 1, 2024, 1-20. doi: 10.21608/jfca.2023.207861.1016
B. N., N., Waghamore, H. (2024). 'Zeros and Weighted value sharing of q-shift difference-differential polynomials of entire and meromorphic functions', EKB Journal Management System, 15(1), pp. 1-20. doi: 10.21608/jfca.2023.207861.1016
B. N., N., Waghamore, H. Zeros and Weighted value sharing of q-shift difference-differential polynomials of entire and meromorphic functions. EKB Journal Management System, 2024; 15(1): 1-20. doi: 10.21608/jfca.2023.207861.1016

Zeros and Weighted value sharing of q-shift difference-differential polynomials of entire and meromorphic functions

Journal of Fractional Calculus and Applications
Article 2, Volume 15, Issue 1, January 2024, Page 1-20  XML PDF (459.34 K)
Document Type: Regular research papers
DOI: 10.21608/jfca.2023.207861.1016
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Authors
NaveenKumar B. N.1; Harina P Waghamore email 2
1Department of Mathematics, Bangalore university, Bengaluru-560056
2Department of Mathematics, Bangalore University, Bangalore, India
Abstract
In this research work, we investigate the uniqueness problems and distribution of zeroes of q-shift difference-differential polynomials of entire and meromorphic functions having zero order in the complex plane ₵ of the form 〖( f^n P(f) ∆_q (f))〗^((k)) and 〖(g^n P(g) ∆_q (g))〗^((k)), where P(f) is a polynomial with constant coefficients of degree m, which is given in Lemma 2.2 and ∆_q (f) is a q-difference operator defined as ∆_q (f)=f(qz+c)-f(qz), which share a small function φ(z),∞ CM. By considering the concept of weighted sharing introduced by I. Lahiri (Nagoya Math. J. 161 (2001), 193–206), we also investigate the uniqueness problem of q-shift difference-differential polynomials sharing a small function φ(z) with weight L, for the cases L≥2,L=1 and L=0 for a zero ordered entire functions. Our results improve, generalize, and extend earlier results due to Zhao and Zhang (J. Contemp. Math. Anal. 50 (2), 63–69). We have also given suitable examples to justify our results.
Keywords
Uniqueness; Entire and Meromorphic functions; Zero order; Finite order; Small function
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