A question about DC-DC converter and buck converter
I see in buck converter examples that they have fixed/regulated input
  voltage and a fixed output.


Well, a buck regulator will work fine with a range of input voltages after all, it wouldn't be much of a regulator if it required a constant input voltage.


  And since the battery voltage will drop by time output voltage will be
  affected proportionally if I use a buck converter.


No, it's a regulator and produces a regulated output. There are some caveats but generally I think your research into buck regulators is flawed.


  Is there a DC DC converter or a type of buck converter which both
  steps down the input voltage and also regulates it to a reference
  value?


Yes, pretty much all of them. Here's an example: -



It will produce 5 volts (at up to 1 amp) at the output with input voltages ranging from 6.5 volts to 100 volts.