  The set of volumes of stable surfaces does have accumulation points. In this
paper, we study this phenomenon for surfaces with one cyclic quotient
singularity, towards answering the question under which conditions we can still
have boundedness. Effective bounds allow listing singularities that might
appear on a stable surface after fixing its invariants. We find optimal
inequalities for stable surfaces with one cyclic quotient singularity, which
can be used to prove boundedness under certain conditions. We also introduce
the notion of generalized T-singularity, which is a natural generalization of
the well-known T-singularities. By using our inequalities, we show how the
accumulation points of volumes of stable surfaces with one generalized
T-singularity are formed.
