Check JS function when its stored in a variable with arguments

I currently store a function in a variable, and then call it:

var function_name = 'test_function';


// some other JS here    


if (typeof app[function_name] != 'undefined') {
     app[function_name];
}


app.test_function = function() {
    alert('woo');
};

This works fine, but what if I store arguments in the function name variable? Like this:

var function_name = 'test_function("mike")';


// some other JS here    


if (typeof app[function_name] != 'undefined') {
     app[function_name];
}


app.test_function = function(name) {
    alert(name);
};

This doesn't work, because typeof app[function_name] is undefined. How can I do this?