I can't update my applications on the iTunes and apple store

Depending on if your device has the ability to see a new iOS, then

you may be able to update or upgrade to later versions of apps.

If your device cannot go past some older iOS due to hardware limit,

then you may not see any update to existing apps; except perhaps

there may be security update for some system apps or browser.

Update your iPhone, iPad, or iPod touch - Apple Support

Learn how to update your iPhone, iPad, or iPod touch

to the latest version of iOS—wirelessly or using iTunes.

https://support.apple.com/en-us/HT204204

What kind of apps were you attempting to get new or updated versions?

As suggested, use the App store in your iOS device for available apps.

• Apps - Official Apple Support:

All topics, resources, & options you need for Apple apps.

Because your thread appears in iPhone, if the phone is older it won't see

update or upgrade to later iOS. My old iPhone 5C won't go past iOS10.3.x

and my old iPad Mini1.1 wi-fi can't use newer than its last iOS9.3.x.

Download apps and games using the App Store - Apple Support

Use the App Store to ... Through the App Store, you can download new apps

for your iOS ... Your Apple ID is the account that you use to access ...

https://support.apple.com/en-us/HT204266

How to Get Missing Apps Back on Your iPhone - Lifewire

Sometimes, it's possible for apps like Safari, Camera, or App Store to disappear

from your iPhone... Lifewire How to Get Missing... kind of content you can access ...

https://www.lifewire.com/app-store-missing-from-iphone-how-to-get-...

Without details, the suggestions would be based on obvious possibilities.

Good luck & happy trails! 🙂

On your device:

Use App Store app.