The installation file was probably not fully downloaded. Try downloading Yandex.Browser again.
If you have access to the network but the problem with updating still exists, update the browser manually. To do this, download the latest browser version and install it over the version that is installed on your computer.
If you get an error message telling you that you need appindicator1, manually download and install the python-appindicator library. Just enter the following command in the console:
apt-get install python-appindicator
Or use the graphic search interface to install the program and find the library by name.