You can make both mobile Chrome and mobile Safari display a native app install banner. The banner suggests that the user installs an app that is related to the current page. It is shown in the phone's native UI. See attached animation.

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There is some fineprint you need to read to make this work (see below).

References

• Android: Increasing engagement with Web App install banners Show archive.org snapshot
• iOS: Promoting Apps with Smart App Banners Show archive.org snapshot