Uniqueness of a Meromorphic Function Partially and Normally Sharing Small Functions with Its Different Variants of Generalized Operator

摘要

First of all, in continuation of our previous result related to "2 CM+1IM" small functions sharing of a meromorphic function of restricted hyper order and its linear shift delay differential operator, in some extend we have been able to answer a question paused by us in [Rendiconti del Circolo Mat. di Palermo, 2021 (Published online)]. As another attempt we improve and extend a result of [Comput. Methods Funct. Theory, 22 (2), 197-205(2022)]. Most importantly, we have pointed out a gap in the proof of a recent theorem [Results Math., 76, 147 (2021)] and citing a proper example we have shown that the result is true only for a particular case. Finally, we present the compact version of the same result as an improvement.