PHP: Calling a user-defined function inside constructor?

There is no difference between calling a function inside a constructor and calling from somewhere else. If the method is declared in the same class you should use $this->function()

By the way, in php5 you are suggested to name your constructor like this:
function __construct()

If not then put public keyword before your constructor definition like this public function userAuth()

$this->nameOfFunction()

But when they are in a class, they are called Methods.

Be careful with using $this in a constructor, though, because in an extension hierarchy, it can cause unexpected behaviour:

<?php

class ParentClass {
    public function __construct() {
        $this->action();
    }

    public function action() {
        echo 'parent action' . PHP_EOL;
    }
}

class ChildClass extends ParentClass {
    public function __construct() {
        parent::__construct();
        $this->action();
    }

    public function action() {
        echo 'child action' . PHP_EOL;
    }
}

$child = new ChildClass();

Output:

child action
child action

Whereas:

class ParentClass {
    public function __construct() {
        self::action();
    }

    public function action() {
        echo 'parent action' . PHP_EOL;
    }
}

class ChildClass extends ParentClass {
    public function __construct() {
        parent::__construct();
        self::action();
    }

    public function action() {
        echo 'child action' . PHP_EOL;
    }
}

$child = new ChildClass();

Output:

parent action
child action