How can I get the application's icon from the package name?

Try this:

try
{
    Drawable icon = getContext().getPackageManager().getApplicationIcon("com.example.testnotification");
    imageView.setImageDrawable(icon);
}
catch (PackageManager.NameNotFoundException e)
{
    e.printStackTrace();
}

if you want to get icon (picture) of any installed application from there packagename, then just copy and paste this code. it will work

try
{
    Drawable d = getPackageManager().getApplicationIcon("com.AdhamiPiranJhandukhel.com");
    my_imageView.setBackgroundDrawable(d);
}
catch (PackageManager.NameNotFoundException e)
{
    return;
}

This also works:

try
{
    Drawable d = getPackageManager().getApplicationIcon(getApplicationInfo());
    my_imageView.setBackgroundDrawable(d);
}
catch (PackageManager.NameNotFoundException e)
{
    return;
}