Communications of the
Korean Mathematical Society CKMS

In this paper, our focus is on exploring value sharing \linebreak problems related to a transcendental entire function $f$ and its associated differential-difference polynomials. We aim to establish some results which are related to differential-difference counterpart of the Br\"{u}ck conjecture.

Keywords: Shared value, shift, difference operator, meromorphic function, uniqueness theory, Br\"{u}ck conjecture

MSC numbers: Primary 39A10, 30D35

Supported by: The research work of Md. Adud is supported by University Grants Commission (India) with Award letter no 424608(CSIR UGC NET JUNE 2017). The research work of Dr.~Bikash Chakraborty is supported by the Department of Higher Education, Science and Technology \text{\&} Biotechnology, Govt.~of West Bengal under the sanction order no.~1303(sanc.)/STBT-11012(26)/17/2021-ST SEC dated 14/03/2022.