It is not a problem of arrow function but using it inside class declaration, this code will work in constructor body or any other function body but not in class declaration.
Code should look just like that:
handleUpdateInput(value){
this.setState({
dataSource: [
value,
value + value,
value + value + value,
],
});
};
Using arrow function can be done inside any class method, but not inside class declaration. For example using arrow function in constructor:
constructor(props,context){
super(props,context);
this.someFunc = ()=>{
//here function code
};
}