バインシステム平井と申します。

漢字設定の返答ありがとうございます。my.cnfを編集しまして
起動しましたら以下のエラーがでました。

ERROR 2002: Can't connect to local MySQL server through socket '/tmp/mysql.sock' (111)

実行スクリプトは以下の内容です。
-------------------------------------
#!/bin/sh
# Copyright Abandoned 1996 TCX DataKonsult AB & Monty Program KB & Detron HB
# This file is public domain and comes with NO WARRANTY of any kind

# Mysql daemon start/stop script.

# Usually this is put in /etc/init.d (at least on machines SYSV R4 based
# systems) and linked to /etc/rc3.d/S99mysql and /etc/rc0.d/S01mysql.
# When this is done the mysql server will be started when the machine is
# started and shut down when the systems goes down.

# Comments to support chkconfig on RedHat Linux
# chkconfig: 2345 90 90
# description: A very fast and reliable SQL database engine.

# The following variables are only set for letting mysql.server find things.
# If you want to affect other MySQL variables, you should make your changes
# in the /etc/my.cnf or other configuration files.

PATH=/sbin:/usr/sbin:/bin:/usr/bin
export PATH

# Set some defaults
datadir=/usr/local/plesk/mysql/var
basedir=
pid_file=
if test -z "$basedir"
then
  basedir=/usr/local/plesk/mysql
  bindir=/usr/local/plesk/mysql/bin
else
  bindir="$basedir/bin"
fi
if test -z "$pid_file"
then
  pid_file=$datadir/`/bin/hostname`.pid
else
  case "$pid_file" in
    /* ) ;;
    * )  pid_file="$datadir/$pid_file" ;;
  esac
fi

mode=$1    # start or stop

parse_arguments() {
  for arg do
    case "$arg" in
      --basedir=*)  basedir=`echo "$arg" | sed -e 's/^[^=]*=//'` ;;
      --datadir=*)  datadir=`echo "$arg" | sed -e 's/^[^=]*=//'` ;;
      --pid-file=*) pid_file=`echo "$arg" | sed -e 's/^[^=]*=//'` ;;
    esac
  done
}

# Get arguments from the my.cfg file, groups [mysqld] and [mysql_server]
if test -x ./bin/my_print_defaults
then
  print_defaults="./bin/my_print_defaults"
elif test -x $bindir/my_print_defaults
then
  print_defaults="$bindir/my_print_defaults"
elif test -x $bindir/mysql_print_defaults
then
  print_defaults="$bindir/mysql_print_defaults"
else
  # Try to find basedir in /etc/my.cnf
  conf=/etc/my.cnf
  print_defaults=
  if test -r $conf
  then
    subpat='^[^=]*basedir[^=]*=\(.*\)$'
    dirs=`sed -e "/$subpat/!d" -e 's//\1/' $conf`
    for d in $dirs
    do
      d=`echo $d | sed -e 's/[  ]//g'`
      if test -x "$d/bin/my_print_defaults"
      then
        print_defaults="$d/bin/my_print_defaults"
        break
      fi
      if test -x "$d/bin/mysql_print_defaults"
      then
        print_defaults="$d/bin/mysql_print_defaults"
        break
      fi
    done
  fi

  # Hope it's in the PATH ... but I doubt it
  test -z "$print_defaults" && print_defaults="my_print_defaults"
fi

parse_arguments `$print_defaults $defaults mysqld mysql_server`

# Safeguard (relative paths, core dumps..)
cd $basedir

case "$mode" in
  'start')
    # Start daemon

    if test -x $bindir/safe_mysqld
    then
      # Give extra arguments to mysqld with the my.cnf file. This script may
      # be overwritten at next upgrade.
      $bindir/safe_mysqld --datadir=$datadir --pid-file=$pid_file &
      # Make lock for RedHat / SuSE
      if test -w /var/lock/subsys
      then
        touch /var/lock/subsys/mysql
      fi
    else
      echo "Can't execute $bindir/safe_mysqld"
    fi
    ;;

  'stop')
    # Stop daemon. We use a signal here to avoid having to know the
    # root password.
    if test -f "$pid_file"
    then
      mysqld_pid=`cat $pid_file`
      echo "Killing mysqld with pid $mysqld_pid"
      kill $mysqld_pid
      # mysqld should remove the pid_file when it exits, so wait for it.

      sleep 1
      while [ -s $pid_file -a "$flags" != aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa ]
      do
        [ -z "$flags" ] && echo "Wait for mysqld to exit\c" || echo ".\c"
        flags=a$flags
        sleep 1
      done
      if [ -s $pid_file ]
         then echo " gave up waiting!"
      elif [ -n "$flags" ]
         then echo " done"
      fi
      # delete lock for RedHat / SuSE
      if test -f /var/lock/subsys/mysql
      then
        rm /var/lock/subsys/mysql
      fi
    else
      echo "No mysqld pid file found. Looked for $pid_file."
    fi
    ;;

  *)
    # usage
    echo "usage: $0 start|stop"
    exit 1
    ;;
esac

------------------------------------------------
エラーの内容から調べても分かりませんでした。
申し訳ないですが分かる方、教えてきただけませんか？