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Study of Br{\"u}ck conjecture and uniqueness of rational function and differential polynomial of a meromorphic function

Dilip Chandra Pramanik|Jayanta Roy
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2022.06|한국수학논문집 (Korean Journal of Mathematics)|제30권 제2호|pp. 249-261

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참고문헌

키워드

Nevanlinna theoryDifferential polynomialWeighted sharingUniqueness.
주제분류수학

초록

Let $f$ be a non-constant meromorphic function in the open complex plane $\mathbb{C}$. In this paper we prove under certain essential conditions that $R(f)$ and $P[f]$, rational function and differential polynomial of $f$ respectively, share a small function of $f$ and obtain a conclusion related to $Br\ddot{u}ck$ conjecture. We give some examples in support to our result.

Abstract

Let $f$ be a non-constant meromorphic function in the open complex plane $\mathbb{C}$. In this paper we prove under certain essential conditions that $R(f)$ and $P[f]$, rational function and differential polynomial of $f$ respectively, share a small function of $f$ and obtain a conclusion related to $Br\ddot{u}ck$ conjecture. We give some examples in support to our result.

참고문헌 (17)

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관련 논문AI추천

Brück Conjecture for a linear differential polynomialBipul Pal, Indrajit Lahiri대한수학회 · 대한수학회논문집2018 · 제33권 제3호Some results related to differential-difference counterpart of the Br\"{u}ck conjectureBikash Chakraborty, Md. Adud대한수학회 · 대한수학회논문집2024 · 제39권 제1호Meromorphic Function that Shares One Small Function with its Differential PolynomialLian-Zhong Yang, Nan Li경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2010 · 제50권 제3호A Further Result Related to a Conjecture of R. BruckKai Liu, Lian-Zhong Yang, Nan Li경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제2호Meromorphic Functions Sharing a Small Function with their Differential PolynomialsJilong Zhang경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2010 · 제50권 제3호Some results on complex differential-difference analogue of Bruck conjectureMin Feng Chen, Zong Sheng Gao대한수학회 · 대한수학회논문집2017 · 제32권 제2호

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