  In this work zero-temperature phase diagrams of cuprates with
Ba$_2$CuO$_3$-type CuO chain structure is investigated. The projective symmetry
group analysis is employed in the strong coupling limit, and renormalization
group with bosonization analysis is employed in the weak coupling limit. We
find that in both of these two limits, large areas of the phase diagrams are
filled with nodeless $s$-wave superconducting phases (with weak $d$-wave
components), instead of pure $d$-wave phase mostly found in cuprates. This
implies that nodeless $s$-wave phase is the dominant superconducting phase in
cuprates with Ba$_2$CuO$_3$-type CuO chain structure in low temperature. Other
phases are also found, including $(s+d)$-wave superconducting phases and
Luttinger liquid phases.
