How to resize images in a slideshow for a Responsive Theme?
You can use Flex Slider either alone, or in combination with FlexSlider Views Slideshow (which provides integration with Views Slideshow in case you already use that one).

Flex Slider module integrates the Flex Slider library with Drupal and allows you to build responsive and resizable slideshows. You'll find plenty of documentation on the project page to fit it to your needs.