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

Molla Basir Ahamed

doi:10.5666/KMJ.2020.60.2.387

Article

Kyungpook Mathematical Journal 2020; 60(2): 387-399

Published online June 30, 2020 https://doi.org/10.5666/KMJ.2020.60.2.387

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

Molla Basir Ahamed

Department of Mathematics, Kalipada Ghosh Tarai Mahavidyalaya, Bagdogra, West Bengal, 734014, India
e-mail : bsrhmd117@gmail.com

Received: April 7, 2018; Revised: June 27, 2019; Accepted: November 28, 2019

Abstract

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Abstract

In this paper, we study a problem of a non-constant entire function f that shares a set 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 Chang-Fang-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 Brück conjecture [9] with the idea of set sharing.

Keywords: normal families, entire functions, set sharing, derivative