Finite-Order Transcendental Entire Solutions of Generalized Non-linear Shift Equations

We have found out the form of the most generalized non-linear shift equations possessing finite-order transcendental entire solutions. We have extended two main results of Qi et al. (Adv. Differ. Equ. 256, 1–10, 2014). We have also pointed out some gaps in the proofs of two theorems in Latreuch (Mediterr. J. Math. 14(3), Art. 115, 2017) and showed that the results are partially true. In an attempt to rectify those results, we have presented their extended corrected forms in a compact manner. Finally, we have presented one more theorem relevant with our other results. A number of examples have been provided by us as and when required.