PHP

if user logged in wordpress

if ( is_user_logged_in() ) {
   // your code for logged in user 
} else {
   // your code for logged out user 
}

how to check if user is logged in wordpress

<?php 
if ( is_user_logged_in() ) {
  echo 'Welcome, logged in user. <a href="'.wp_logout_url().'">Click here to logout</a>.';
}else{
  echo 'Please login by <a href="'.wp_login_url().'">clicking here</a>.'
}

if user name is wordpress

<?php
add_action('admin_init', 'wpse74389_check_username');
function wpse74389_check_username()
{
    $user = wp_get_current_user();

    if($user && isset($user->user_login) && 'username_to_check' == $user->user_login) {
        // do stuff
    }
}