Demo

var divs = $('#elements div');
var links = $('#elements div a');

1. If you want the DOM elements, then you can access them with the array style like divs[0] or links[2].
2. If you want to get the specific jQuery object, you can access them with divs.eq(0) or links.eq(1).

Try this:

$("li").map(function(){ return this.innerText })

or this:

$("li").toArray().map(function(i){ return i.innerText })

As bpierre suggested, use .map(). His answer is correct.

If you need this behavior for different attributes, you might as well write is as a reusable function (“jQuery plugin”):

jQuery.fn.pluck = function(attr) {
  return this.map(function() {
    return this.getAttribute(attr);
  }).get();
};

$('input:checkbox:checked').pluck('category_uid'); // ["1.3", "1.3.1"]

P.S. category_uid is not a valid attribute in HTML. Consider using custom data-* attributes instead, e.g. data-category-uid="foo".

Without redundant intermediate arrays:

var arr = $('li').map(function(i,el) {
    return $(el).text();
}).get();

See jsfiddle demo

You should use:

card_value=  array.eq(i).val(); //gets jquery object at index i

or

card_value=  array[i].value; //gets dom element at index i

Your "html array" is not an array at all, even assuming there are a number of other similar inputs (though when the form is submitted your chosen server-side language likely lets you access the values of inputs with the same name as an array). Anyway...

The main problem is that your JS has a syntax error:

$("input[id^="author"]")

If you want to include double-quotes inside a double-quoted string literal you have to do escape them:

$("input[id^=\"author\"]")

Or quote the string with singles:

$('input[id^="author"]')

It may be more efficient to avoid the attribute starts-with selector with the id attribute and select by the name attribute, noting that for jQuery the square brackets in the atttribute name need to be escaped with backslashes, and for JS string literals backslashes also need to be escaped:

$('input[name="authors\\[\\]"]')

Also to get the value of an input with jQuery use .val() rather than .text(), but it is more efficient to just use this.value:

var authors = [];
$('input[id^="author"]').each(function(){ authors.push(this.value); }); 

I'd also recommend declaring arrays with = [] rather than = new Array().

You can iterate through the object keys and save the name in the array using push:

example = [{
  name: "someone1",
  city: "somewhere1",
  state: "someplace1"
}, {
  name: "someone2",
  city: "somewhere2",
  state: "someplace2"
}];
var arrNames = [];
//iterate through object keys
Object.keys(example).forEach(function(key) {
  //get the value of name
  var val = example[key]["name"];
  //push the name string in the array
  arrNames.push(val);
});
console.log(arrNames);//prints ["someone1", "someone2"]

After @Felix suggestion(with which I agree) there is no need to use Object.keys:

example = [{
  name: "someone1",
  city: "somewhere1",
  state: "someplace1"
}, {
  name: "someone2",
  city: "somewhere2",
  state: "someplace2"
}];
var arrNames = [];
//iterate through object keys
example.forEach(function(item) {
  //get the value of name
  var val = item.name
  //push the name string in the array
  arrNames.push(val);
});
console.log(arrNames); //prints ["someone1", "someone2"]

References

Object.keys()

Array.prototype.forEach()

Array.prototype.push()

const textValues = $.map($('input[type=text][name="pages_title[]"]'), function(el) { return el.value; });
   console.log(textValues);

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<input type="text" value="Hello" name="pages_title[]">
<input type="text" value="World" name="pages_title[]">

If you call .get() on a jQuery object without a parameter, it will return a regular array of DOM elements.

var arrayForPrice = {
"93":{"id":"93","code":"color","label":"Color","options":[{"id":"50","label":"Blue","products":["1216","1219","1222"]},{"id":"58","label":"Red","products":["1217","1220","1223"]},{"id":"60","label":"Yellow","products":["1218","1221","1224"]}],"position":"1"},
"141":{"id":"141","code":"size","label":"Size","options":[{"id":"168","label":"S","products":["1216","1217","1218"]},{"id":"169","label":"M","products":["1219","1220","1221"]},{"id":"170","label":"L","products":["1222","1223","1224"]}],"position":"0"}
};


for(var i in arrayForPrice){
	console.log(arrayForPrice[i].options);
}