On Uniqueness of Meromorphic Functions Partially Sharing Values with Their q-shifts

In this work, we give some uniqueness theorems for non-constant zero-order meromorphic functions when they and their q-shifts partially share values in the extended complex plane. This is a continuation of previous works of Charak et al. (J Math Anal Appl 435(2):1241-1248, 2016) and of Lin et al. (Bull Korean Math Soc 55(2):469-478, 2018). Furthermore, we show some uniqueness results in the case multiplicities of partially shared values are truncated to level m >= 4. As a consequence, we obtain a uniqueness result for an entire function of zero-order if it and its q-shift partially share three distinct values a(1),a(2),a(3) without truncated multiplicities, in which we do not need to count a(j)-points of multiplicities greater than 38 for all j=1,2,3.