I asked what version of shell you're using, but you didn't provide an answer to that question. With a recent Korn shell, such as version 93u+, (which may be installed as ksh93 on AIX 7.1) you could try a simplified version of:
for file in "$@"
printf 'File: %s: %(%a(%w), %Y-%m-%d)T, Previous Tuesday: %(%Y%m%d\n)T' \
"$file" "$fd" "$fd $((($(printf '%(%u)T' "$fd")+5)%7)) days ago"
which if invoked with the operands FILE_NAME_20180410, FILE_NAME_20180413, and FILE_NAME_20180409 produces the output: