Jon Tejnung

This plugin will give you three alternatives for managing your WordPress updates:
<ul>
<li>Update automatically – This updates WordPress/themes/plugins automatically and sends an email to the site admin when an update has been performed.</li>
<li>Update automatically (no email) – Same as the first alternative, but without the email.</li>
<li>Inform about updates once a week – This will send an email to the admin once a week if there are anything that can be updated.</li>
</ul>
Notice that only plugins/themes that resides in the WordPress 
repository will be updated/informed about.
The plugin has not been tested and is not primarily made for multi site-installations.

Simple Automatic Updates

Activate automatic updates or weekly notifications for the site.

Scott Reilly

Tired of visiting your WordPress admin dashboard and having WordPress nag you about your web browser being out of date? Maybe you already know about it and want to hold off on an update and would rather not see the update nag so prominently on your dashboard. Or maybe you don’t want your site to bother your users about how up-to-date their browser may be. Activate this plugin and be bothered no more!
In most cases, your browser will already actively alert you to new releases if it doesn’t already update your browser for you in the background.
Benefits over simply clicking “dismiss” on the browser nag notice yourself when it appears:
<ul>
<li>This plugin prevents WordPress from making the network request to check if the browser is out of date. If you click “dismiss”, all you’re doing is hiding the nag; WordPress will still make the network request to check if the browser is out of date.</li>
<li>This plugin prevents the nag from appearing for all users to the admin area of the site. Clicking “dismiss” only removes the nag for the person dismissing it.</li>
<li>This plugin saves having to see the nag in the first place</li>
<li>This plugin saves having to click “Dismiss” to dismiss the nag</li>
</ul>
Of course I don’t condone using an out-of-date browser. Such a browser puts your computer and data at potential risk. You are often better served with the latest version of your browser: improved security, improved performance, improved stability, and additional features. However, there are situations where you cannot upgrade in a timely fashion, or you are intentionally holding off on upgrading (e.g. as you wait for a bugfix release, or for browser plugins to update their compatibility).
Links: <a href="https://coffee2code.com/wp-plugins/no-browser-nag" rel="nofollow ugc">Plugin Homepage</a> | <a href="https://wordpress.org/plugins/no-browser-nag/" rel="ugc">Plugin Directory Page</a> | <a href="https://github.com/coffee2code/no-browser-nag/" rel="nofollow ugc">GitHub</a> | <a href="https://coffee2code.com" rel="nofollow ugc">Author Homepage</a>

No Browser Nag

Removes the browser nag that appears in the admin dashboard when using a less-than-current web browser.

Simple Automatic Updates vs No Browser Nag