Vlad Sure, here are some examples from the DuckDuckGo app:
Here's the search widget on the homescreen. It's really just an extra-wide button that opens the search UI. (Ignore the bottom Google search box, it can't be removed and isn't relevant here.)
When you click the widget, you get this interface with the search box and the autosuggest results. It's a native app, so it opens immediately and is more responsive than a web page.
The DuckDuckGo app then opens its results in its own full-featured web browser, but I'd personally prefer if the Kagi results opened directly as a single results page in the app (like the Google app) or just opened my default browser to the results page.