You can write weekday names in lower case and then change the case of the user input to lower before searching. There's a function tolower or something like this to do that.
#include <iostream>
#include <string>
#include <map>
using namespace std;
int main()
{
string day;
cout << "This program will tell you your schedule for the next week.\nEnter a day: \n";
cin >> day;
transform(day.begin(), day.end(), day.begin(), [](unsigned char a) { return tolower(a); });
map<string, string> mymap = {{"saturday", "Offday. Enjoy"}, {"sunday", "Offday. Enjoy"}, {"monday", "Morning duty at the department"}, {"tuesday", "24 hours duty."}, {"wednesday", "Offday. Enjoy."}, {"thurusday", "Morning duty at the OPC"}, {"friday", "Offday. Enjoy."}};
auto it = mymap.find(day);
if (it != mymap.end())
{
cout << "Your schedule for " << day << ":\n";
cout << it->second;
}
else
{
cout << "You entered wrong day.\n";
}
}