It seems that i cannot access $(this) inside jquery ajax success function. please see below code.
 $.ajax({
            type: 'post',
            url: '<?php echo site_url('user/accept_deny_friendship_request')?>',
            data: 'action='+$action+'&user_id='+$user_id,
            success: function(response){
               //cannot access $(this) here $(this).parent().remove();
            }
        });