MySQLUpdate内部結合テーブルクエリ

これを試してください：

UPDATE business AS b
INNER JOIN business_geocode AS g ON b.business_id = g.business_id
SET b.mapx = g.latitude,
  b.mapy = g.longitude
WHERE  (b.mapx = '' or b.mapx = 0) and
  g.latitude > 0

更新：

クエリで構文エラーが発生したとおっしゃっていたので、テストできるテーブルをいくつか作成し、クエリに構文エラーがないことを確認しました。

mysql> create table business (business_id int unsigned primary key auto_increment, mapx varchar(255), mapy varchar(255)) engine=innodb;
Query OK, 0 rows affected (0.01 sec)

mysql> create table business_geocode (business_geocode_id int unsigned primary key auto_increment, business_id int unsigned not null, latitude varchar(255) not null, longitude varchar(255) not null, foreign key (business_id) references business(business_id)) engine=innodb;
Query OK, 0 rows affected (0.01 sec)

mysql> UPDATE business AS b
    -> INNER JOIN business_geocode AS g ON b.business_id = g.business_id
    -> SET b.mapx = g.latitude,
    ->   b.mapy = g.longitude
    -> WHERE  (b.mapx = '' or b.mapx = 0) and
    ->   g.latitude > 0;
Query OK, 0 rows affected (0.00 sec)
Rows matched: 0  Changed: 0  Warnings: 0

見る？構文エラーはありません。 MySQL5.5.8に対してテストしました。