Q:

Calling a constructor of included class within class constructor

In class argList constructor is the instruction
args_[0] = fileName(argv[0]);

When searching for method fileName(...) it turns out that it should be a constructor of class fileName:
inline Foam::fileName::fileName(const char* str) //Construct as copy of character array. 
: string(str)    //Construct as copy of character array. 
{
    stripInvalid();    //Strip invalid characters from the given string. 
}

Two Questions:

Is it really the constructor of class fileName that is called? 
Hasn' t the constructor of fileName to be static if it was called
like this? 

greetings
streight

A:

Yes - this is a really constructor of fileName class - there's no return value and the name of the method is the same as the name of the class. 
This is not a call to the constructor, but the definition of the constructor (I guess :: is what is confusing you):
inline Foam::fileName::fileName(const char* str) //Construct as copy of character array. 

This is the call to the constructor:
args_[0] = fileName(argv[0]);

There's no static constructor in C++. 

A:

'1.  Is it really the constructor of class fileName that is called? 

Yes.  The constructor is called because it args_[0] is assigned a new instance of the fileName class. 

'2.  Hasn' t the constructor of fileName to be static if it was called like this? 

No.  A constructor cannot be static.  This is one of the correct ways to construct objects.