Uniqueness Result Concerning First Derivative and Difference of a Meromorphic Function andSufficient Condition for Periodicity

Pub Date : 2024-07-09 DOI:10.3103/s1068362324700109

S. Majumder, N. Sarkar

引用次数: 0

Abstract

In the paper, we discuss the uniqueness problem of meromorphic function \(f(z)\) when \(f^{\prime}(z)\) shares \(a\), \(b\) and \(\infty\) CM with \(\Delta_{c}f(z)\), where \(a\) and \(b\) are two distinct finite values. The obtained result improves the recent result of Qi et al. [6] by dropping the condition ‘‘order of growth of \(f\) is not an integer or infinite’’ by ‘‘\(\rho(f)<\infty\)’’. Also in the paper we give an affirmative answer of the question raised by Wei et al. [9].

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关于一次函数的一阶导数和差分的唯一性结果以及周期性的充分条件

Abstract 本文讨论了当\(f^{\prime}(z))与\(\Delta_{c}f(z)\)共享\(a\)、\(b\)和\(\infty\)CM，其中\(a\)和\(b\)是两个不同的有限值时，并变函数\(f(z)\)的唯一性问题。所得到的结果改进了齐等人最近的结果[6]，放弃了"'\(f)的增长阶数不是整数或无限'"的条件，改为"'\(\rho(f)<\infty\)'"。在本文中，我们还对 Wei 等人[9]提出的问题给出了肯定的答案。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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