Is it possible to Resize the image double to its original size(image is small in size, example, 80px by 80px, size of an icon), without being blurred. I have tried every type of sharpening technique but still not got the desired output and please tell which sharpening technique is better?
The choice of scaling techniques highly depends on your input image. There are various techniques available (GIMP has most of them), but no single one is perfect.
The problem is that you always have to blur the image, since you are trying to double the amount of information in the image. Every scaling technique has some way of determining the color of a new pixel.
When looking for the color of a pixel, choose the nearest possible pixel from the original image. Good for hard edges, but only for horizontal and vertical lines.
Choose the next two possible pixels and interpolate between them. Better for photos, but causes blurring and introduces artifacts on lines that are not horizontal or vertical.
Approximate third-degree polynoms between the source pixels and evaluate them for every requested pixel. Makes for smooth edges, good for photos, bad for images with hard edges.
More techniques are explained on Wikipedia.
Your best option would be to retrieve a higher-quality image to start with. If you have vector-images of your icons, you can simply export those with a higher resolution.
Despite the impression that movies and TV series give these days, there is no way to get arbitrary bitmap image significantly enlarged without getting ugly artifacts and/or blurry appearance. The reason is simply the fact that there is no way to make up the +300% of additional information (I take your example of "doubling" mean doubling the height and width of the image) required for the operation from the original image. With vector image formats (SVG etc) the story is completely different, though, and that is one of the main causes we have such formats.
It is possible to have algorithms that recognise patterns and shapes in the original pixel array and based on that information they could produce much smoother zoom-up, but that would not be feasible on arbitrary image data that is not composed of simple patterns on smooth background. Sharpening only attempts to make blurry edges look more sharp by increasing the contrast on edges, but that doesn't bring any extra information to the image, either, it is more aimed at helping human vision pick the details from the image.
As far as I know, there are no good tools in Gimp (at least built-in) that could do what you want. However, if you find a tool for the task, please tell me since I'm currently in need of such myself...
However, there are applications that try to convert a bitmap into a vector image, which would free you from the limitations of bitmaps regarding scaling. See e.g. How To Enlarge Images Without Losing Quality or Pixelated, Enlarge Images Without Losing Quality – 4 Tools and How to convert poor quality bitmap image to vector?. Inkscape is a free software that can do that, also many commercial options exist.
Then there are a couple of online vectorisation services. Vector Magic seems to do terrific job at converting an icon to a vector drawing - the downside being that it seems to offer only two downloads from free (well, I can't blame anyone for trying to earn some bucks out of what seems to be a good service). AutoTracer is free-of-charge, but at least the results for my pics were not good (even after several attempts with tweaked conversion settings).