When I assign an item to more than one person in Jira, the people I assign are not notified, the item is not displayed in their assigned items list and the item appears unassigned. how can I fix this problem
Jira doesn't allow you to assign issues to more than one user. I suspect you are using a multi-user custom field or a plugin so the behavior isn't what you are expecting.
As Joe mentions, the concept of multi user assignment is not an out of the box feature.
Meaning a custom field was used (single user, multi select) or some plugin that offers the functionality.
99% certain neither of these will provide a notification to the users by default. Depending on how it was implemented tho you might be able to leverage Automation to send notifications using a rule with the "send email" action
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