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Set shared by an Entire Function with its k-th Derivative Using Normal Families

Molla Basir Ahamed
경북대학교 자연과학대학 수학과|2020.06|Kyungpook Mathematical Journal|제60권 제2호|pp. 387-399|DOI 10.5666/KMJ.2020.60.2.387

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키워드

derivativenormal familiesset sharingentire functions
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초록

In this paper, we study a problem of a non-constant entire function f that shares a set S = {a,b,c}with its k-th derivative f^(k), where a,b and c are any three distinct complex numbers. We have found a gap in the statement of the main result of ChangFang-Zalcman [10], and with the help of their method, we have generalize their result in a more compact form. As an application, we generalize the famous Bruck conjecture [9] with the idea of set sharing.

Abstract

In this paper, we study a problem of a non-constant entire function f that shares a set S = {a,b,c}with its k-th derivative f^(k), where a,b and c are any three distinct complex numbers. We have found a gap in the statement of the main result of ChangFang-Zalcman [10], and with the help of their method, we have generalize their result in a more compact form. As an application, we generalize the famous Bruck conjecture [9] with the idea of set sharing.

참고문헌 (26)

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관련 논문AI추천

Further Results about the Normal Family of Meromorphic Functions and Shared SetsGuowei Zhang, Jianming Qi, Linlin Zhou경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2012 · 제52권 제1호Normality concerning two families of meromorphic functionsBanarsi Lal, Virender Singh대한수학회 · 대한수학회논문집2020 · 제35권 제4호Normality criteria for a family of meromorphic functions with multiple zerosGopal Datt, Poonam Rani, Yuntong Li대한수학회 · 대한수학회논문집2018 · 제33권 제3호THE BRUCK CONJECTURE AND ENTIRE FUNCTIONS SHARING POLYNOMIALS WITH THEIR k-TH DERIVATIVESFeng Lu, Hongxun Yi대한수학회 · 대한수학회지2011 · 제48권 제3호Meromorphic Functions Sharing a Nonzero Value with their DerivativesDa-Xiong Piao, Hong-Xun Yi, Rahman ullah, Xiao-Min Li경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제1호A note on the Bruck conjectureFeng Lu대한수학회 · 대한수학회보2011 · 제48권 제5호

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