Variational inequality problem, denoted by VIP(F, C), is one of the fundamental problems in optimization theory. Very often the subset C has a special structure. This subset is often the intersection of simpler to handle closed convex subsets or a sublevel set of a convex function or, more generally, a set of fixed points of a quasi-nonexpansive operator. In this talk we will consider an abstract variational inequality in a real Hilbert space, which covers all of these three cases. For this purpose we will introduce a class of approximately shrinking (AS) operators and discuss their basic properties. Moreover, we will present a few examples of iterative methods with application of AS operators, which can be used to solve VIP(F,C). Iterative schemes which are going to be presented are mostly based on the hybrid steepest descent method introduced by Isao Yamada in 2001 and extended by A. Cegielski and R. Zalas in 2013. These iterative schemes are related to cyclic, sequential and also to string averaging procedures of construction of operators, which are more general.