Thanks for the suggestion, which I've tried, but sadly it doesn't work. My problem is not that I can't see any updates waiting for me in the App Store, on the Updates page. On the contrary, I've now got four of them waiting for me. The problem is that whether I click on 'Update All' or just on an individual 'Update' by one of the updates, the App Store simply won't install any updates for me. Thanks for suggesting that net monitoring or antivirus apps might prevent updates. I have AVG AntiVirus running, but even if I temporarily disable it, the updates won't install.

Use Software Update

Why Can't I Download Java

If you aren’t sure if the “Verifying” process is stuck on the Mac, open the package, disk image, or installer file as usual and let the verification procedure run for a while, it can take many minutes or longer to complete. If the process is still stuck and unchanged an hour or so later, it’s probably stuck. JDK 12 Releases. JDK 12 has been superseded. Please visit jdk.java.net for the current version. Older releases, which do not include the most up to date security. Choose System Preferences from the Apple menu, then click Software Update to check for updates. If any updates are available, click the Update Now button to install them. Or click “More info” to see details about each update and select specific updates to install.

Choose System Preferences from the Apple menu , then click Software Update to check for updates.
If any updates are available, click the Update Now button to install them. Or click “More info” to see details about each update and select specific updates to install. You might be asked to enter your administrator password.
When Software Update says that your Mac is up to date, the installed version of macOS and all of its apps are also up to date. That includes Safari, Music, Photos, Books, Messages, Mail, Calendar, and FaceTime.
To automatically install future updates, including for apps that you got from the App Store, select “Automatically keep my Mac up to date.” Your Mac will notify you when updates require it to restart, so you can always choose to install those later.

Update the software on your iPhone, iPad, or iPod touch

Learn how to update your iPhone, iPad, or iPod touch to the latest version of iOS or iPadOS.

Download Latest Java For Mac

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Why Won't Java Download

Java For Mac Won't Complete Download Free

Learn how to get updates for earlier versions of macOS that don't include Software Update preferences.
You can also use the App Store to update apps or redownload apps that came from the App Store.
Learn which macOS your Mac is using and how to upgrade to the latest macOS.
When your Mac is connected to a Personal Hotspot, large updates don't download automatically.