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Abstract <p>In this paper, we consider the uniqueness problem of sharing a small function between n-th order difference operator <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Delta_{c}^{n}f(z)\)</EquationSource> <!--ContMath2560046Zhang-m1--> </InlineEquation> and first-order difference operator <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Delta_{c}f(z)\)</EquationSource> <!--ContMath2560046Zhang-m2--> </InlineEquation> of a finite order transcendental entire function <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(f(z)\)</EquationSource> <!--ContMath2560046Zhang-m3--> </InlineEquation>. This mainly generalizes the corresponding result due to He et al. [<CitationRef CitationID="CR15">15</CitationRef>].</p>

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Uniqueness Theorems Related to Higher-Order Difference Operators of Entire Functions

  • 期刊论文

  • 发表日期：

    2026年4月18日

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  • J.-X. Zhang,
  • J.-F. Chen

摘要

Abstract

In this paper, we consider the uniqueness problem of sharing a small function between n-th order difference operator \(\Delta_{c}^{n}f(z)\) and first-order difference operator \(\Delta_{c}f(z)\) of a finite order transcendental entire function \(f(z)\) . This mainly generalizes the corresponding result due to He et al. [15].