On the two conjectures
Nabadwip Sarkar, Debabrata Pramanik, Lata Mahato
TL;DR
This paper investigates the uniqueness of entire functions sharing an entire function with their higher-order difference operators, confirming two conjectures and providing illustrative examples.
Contribution
It confirms two conjectures regarding the uniqueness of entire functions sharing with their difference operators, advancing understanding in complex analysis.
Findings
Confirmed two conjectures on entire functions and difference operators
Provided examples supporting the theoretical results
Enhanced understanding of function sharing in complex analysis
Abstract
In this paper, we investigate the uniqueness problem of entire functions that share an entire function with their higher-order difference operators. We obtain two results that confirm the conjectures posed by Liu and Laine \cite{LL1} and by Zhang et al. \cite{ZKL1}, respectively. In addition, we present several relevant examples to further illustrate and support our findings
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Taxonomy
TopicsMeromorphic and Entire Functions · Analytic and geometric function theory · Nonlinear Differential Equations Analysis