It varies depending on the browser and these days the device (tablet, smartphone, etc). But at a minimum, your favicon link should be constructed as follows:
<link rel="icon"
type="image/png"
href="http://example.com/myicon.png">
Currently, your file reference is relative to URI, meaning that if you have pages deeper than one level below your document root, your code is going to break. To illustrate, here's an example:
If you visit http://example.com, the browser will look for your favicon file at http://example.com/myicon.png.
If you visit http://example.com/mycategory/myarticle.html, the browser will look for your favicon file at http://example.com/mycategory/myicon.png, which won't be found.
See the problem? So either use an absolute path to your favicon file:
<link rel="icon"
type="image/png"
href="http://example.com/myicon.png">
or make the path relative to your document root:
<link rel="icon"
type="image/png"
href="/myicon.png">
Looking at the HTML you posted, another obvious problem that stands out is poorly structured (invalid) HTML. Remove the first four lines in your HTML document:
1. HTML
2. <a>
3. <!DOCTYPE html>
4.
The first line is just text and will confuse browsers trying to determine the document type of the page being loaded. The second line is a valid HTML element but it needs to exist within parent
<html>
<body>
...
</body>
</html>
elements. The third line isn't a valid declaration and looks like a stab in the dark, and the fourth is a blank line. If you don't actually know what HTML standard you're coding to, it's probably best to simply omit the DOCTYPE declaration and simply let the browser guess the standard to use because this WILL affect how your HTML is interpreted (and rendered). I don't know if it's universally true, but I think most browsers will fall back to the loosest HTML standard in the absence of a defined DOCTYPE.
One final thought. If you're new to HTML and/or don't have any sort of formal education/training, take some time to go through online tutorials. http://www.w3schools.com is a basic resource that can help you better understand the language.