[javascript] How should I call 3 functions in order to execute them one after the other?

You could also use promises in this way:

    some_3secs_function(this.some_value).then(function(){
       some_5secs_function(this.some_other_value).then(function(){
          some_8secs_function(this.some_other_other_value);
       });
    });

You would have to make some_value global in order to access it from inside the .then

Alternatively, from the outer function you could return the value the inner function would use, like so:

    one(some_value).then(function(return_of_one){
       two(return_of_one).then(function(return_of_two){
          three(return_of_two);
       });
    });

ES6 Update

Since async/await is widely available now, this is the way to accomplish the same:

async function run(){    
    await $('#art1').animate({'width':'1000px'},1000,'linear').promise()
    await $('#art2').animate({'width':'1000px'},1000,'linear').promise()
    await $('#art3').animate({'width':'1000px'},1000,'linear').promise()
}

Which is basically "promisifying" your functions (if they're not already asynchronous), and then awaiting them

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