Reboot the computer and insert the live cd of Fedora.
Open the terminal and type:

# lvm
lvm> vgchange -a y
lvm> exit

sudo fsck -y /dev/mapper/fedora-root

[liveuser@localhost ~]$ fsck
fsck from util-linux 2.23.1
[liveuser@localhost ~]$ fsck -p
fsck from util-linux 2.23.1
[liveuser@localhost ~]$ fsck
fsck from util-linux 2.23.1
[liveuser@localhost ~]$ yum install gparted
Loaded plugins: langpacks, refresh-packagekit
You need to be root to perform this command.
[liveuser@localhost ~]$ sudo yum install gparted

We trust you have received the usual lecture from the local System
Administrator. It usually boils down to these three things:

    #1) Respect the privacy of others.
    #2) Think before you type.
    #3) With great power comes great responsibility.

Loaded plugins: langpacks, refresh-packagekit
fedora/19/x86_64/metalink                                | 8.2 kB     00:00     
fedora                                                   | 4.2 kB     00:00     
updates/19/x86_64/metalink                               | 6.9 kB     00:00     
updates                                                  | 4.9 kB     00:00     
(1/2): updates/19/x86_64/primary_db                        |  12 MB   00:16     
(2/2): fedora/19/x86_64/primary_db                         |  17 MB   00:27     
fedora/19/x86_64/group_gz                                | 384 kB     00:00     
updates/19/x86_64/group_gz                               | 394 kB     00:00     
Resolving Dependencies
--> Running transaction check
---> Package gparted.x86_64 0:0.18.0-1.fc19 will be installed
--> Processing Dependency: polkit-gnome for package: gparted-0.18.0-1.fc19.x86_64
--> Running transaction check
---> Package polkit-gnome.x86_64 0:0.105-4.fc19 will be installed
--> Finished Dependency Resolution

Dependencies Resolved

================================================================================
 Package             Arch          Version                 Repository      Size
================================================================================
Installing:
 gparted             x86_64        0.18.0-1.fc19           updates        1.7 M
Installing for dependencies:
 polkit-gnome        x86_64        0.105-4.fc19            fedora          82 k

Transaction Summary
================================================================================
Install  1 Package (+1 Dependent package)

Total download size: 1.7 M
Installed size: 6.4 M
Is this ok [y/d/N]: y
Downloading packages:
(1/2): polkit-gnome-0.105-4.fc19.x86_64.rpm                |  82 kB   00:00     
gparted-0.18.0-1.fc19.x86_64.r FAILED                                          
http://ftp6.sjtu.edu.cn/fedora/linux/updates/19/x86_64/gparted-0.18.0-1.fc19.x86_64.rpm: [Errno 14] curl#6 - "Could not resolve host: ftp6.sjtu.edu.cn; Name or service not known"
Trying other mirror.
(2/2): gparted-0.18.0-1.fc19.x86_64.rpm                    | 1.7 MB   00:01     
--------------------------------------------------------------------------------
Total                                           198 kB/s | 1.7 MB     00:09     
Running transaction check
Running transaction test
Transaction test succeeded
Running transaction
  Installing : polkit-gnome-0.105-4.fc19.x86_64                             1/2
  Installing : gparted-0.18.0-1.fc19.x86_64                                 2/2
  Verifying  : gparted-0.18.0-1.fc19.x86_64                                 1/2
  Verifying  : polkit-gnome-0.105-4.fc19.x86_64                             2/2

Installed:
  gparted.x86_64 0:0.18.0-1.fc19                                                

Dependency Installed:
  polkit-gnome.x86_64 0:0.105-4.fc19                                            

Complete!
[liveuser@localhost ~]$ gparted
Root privileges are required for running gparted.
[liveuser@localhost ~]$ sudo gparted
======================
libparted : 3.1
======================
[liveuser@localhost ~]$ fsck /dev/sda5
fsck from util-linux 2.23.1
e2fsck 1.42.7 (21-Jan-2013)
fsck.ext2: Permission denied while trying to open /dev/sda5
You must have r/w access to the filesystem or be root
[liveuser@localhost ~]$ sudo fsck
fsck from util-linux 2.23.1
[liveuser@localhost ~]$ sudo fsck --help
fsck from util-linux 2.23.1
[liveuser@localhost ~]$ sudo fsck /dev/sdb2
fsck from util-linux 2.23.1
fsck: fsck.LVM2_member: not found
fsck: error 2 while executing fsck.LVM2_member for /dev/sdb2
[liveuser@localhost ~]$ sudo fsck /dev/sdb1
fsck from util-linux 2.23.1
e2fsck 1.42.7 (21-Jan-2013)
/dev/sdb1: clean, 385/128016 files, 175027/512000 blocks
[liveuser@localhost ~]$ sudo fsck /dev/sdb1
fsck from util-linux 2.23.1
e2fsck 1.42.7 (21-Jan-2013)
/dev/sdb1: clean, 385/128016 files, 175027/512000 blocks
[liveuser@localhost ~]$ sudo fsck /dev/sdb2
fsck from util-linux 2.23.1
fsck: fsck.LVM2_member: not found
fsck: error 2 while executing fsck.LVM2_member for /dev/sdb2
[liveuser@localhost ~]$ lvm
  WARNING: Running as a non-root user. Functionality may be unavailable.
lvm> exit
  Exiting.
[liveuser@localhost ~]$ sudo lvm
lvm> vgchange -a y
  3 logical volume(s) in volume group "fedora" now active
lvm> exit
  Exiting.
[liveuser@localhost ~]$ ls /dev/vgtest/lv0
ls: cannot access /dev/vgtest/lv0: No such file or directory
[liveuser@localhost ~]$ ls /dev/vgtest/lv0
ls: cannot access /dev/vgtest/lv0: No such file or directory
[liveuser@localhost ~]$ fsck /dev/mapper/fedora-root
fsck from util-linux 2.23.1
e2fsck 1.42.7 (21-Jan-2013)
fsck.ext2: Permission denied while trying to open /dev/mapper/fedora-root
You must have r/w access to the filesystem or be root
[liveuser@localhost ~]$ sudo fsck /dev/mapper/fedora-root
fsck from util-linux 2.23.1
e2fsck 1.42.7 (21-Jan-2013)
/dev/mapper/fedora-root contains a file system with errors, check forced.
Pass 1: Checking inodes, blocks, and sizes
Inodes that were part of a corrupted orphan linked list found.  Fix<y>? yes
Inode 1053367 was part of the orphaned inode list.  FIXED.
Inode 1053368 was part of the orphaned inode list.  FIXED.
Inode 1053369 was part of the orphaned inode list.  FIXED.
Inode 1053370 was part of the orphaned inode list.  FIXED.
Pass 2: Checking directory structure
Entry '.readahead' in / (2) has deleted/unused inode 14.  Clear<y>? yes
Pass 3: Checking directory connectivity
Pass 4: Checking reference counts
Pass 5: Checking group summary information
Block bitmap differences:  -3192443 -(5380992--5381077)
Fix<y>? yes
Free blocks count wrong for group #97 (20646, counted=20647).
Fix<y>? yes
Free blocks count wrong for group #164 (10035, counted=10121).
Fix<y>? yes
Free blocks count wrong (8072212, counted=8072299).
Fix<y>? yes
Inode bitmap differences:  -14 -796106 -(1053366--1053370)
Fix<y>? yes
Free inodes count wrong for group #0 (6681, counted=6682).
Fix<y>? yes
Free inodes count wrong for group #97 (6548, counted=6549).
Fix<y>? yes
Free inodes count wrong for group #128 (1558, counted=1563).
Fix<y>? yes
Free inodes count wrong (2951727, counted=2951734).
Fix<y>? yes

/dev/mapper/fedora-root: ***** FILE SYSTEM WAS MODIFIED *****
/dev/mapper/fedora-root: 325066/3276800 files (1.3% non-contiguous), 5034901/13107200 blocks
yyyyyyyyyyy[liveuser@localhost ~]$ fsck -y /dev/mapper/fedora-root
fsck from util-linux 2.23.1
e2fsck 1.42.7 (21-Jan-2013)
fsck.ext2: Permission denied while trying to open /dev/mapper/fedora-root
You must have r/w access to the filesystem or be root
[liveuser@localhost ~]$ sudo fsck -y /dev/mapper/fedora-root
fsck from util-linux 2.23.1
e2fsck 1.42.7 (21-Jan-2013)
/dev/mapper/fedora-root: clean, 325066/3276800 files, 5034901/13107200 blocks
[liveuser@localhost ~]$