Most of taxi drivers in Istanbul are not honest and 50-50 robbers. It's not a general issue but you need to be very careful and remember following points. I don't know how you can claim to the company that manages taxi drivers or to police but I think it's better to prevent:
1- note exchange, some drivers may exchange your 200, 100 or 50 liras to 20, 10 and 5. So check the money before you give it to taxi driver so he can't ask you to exchange it. When you're not sure or confused he can repeat this trick several times.
2- some drivers ask you for 10 liras when the ride is less than 10 for example while the taximeter is showing 6 liras they ask you for 10 (minimum ride). The min ride actually is 4 liras that you can see on taximeter when you get in. So you can and have to pay what you can see on taximeter but I recommend you to pay what driver ask you to pay if you are with family and child.
3- if you are in a taxi and taximeter is off, ask the driver to turn it on immediately and if driver find an excuse for that ask how much does it cost till your destination and if it doesn't seem logical get off the taxi immediately and pay 10 liras or less. For example once a taxi driver (taximeter off) answered that we need to pay 70 to 80 liras for a ride from Sisly to Sulimaniye. We immediately get off and paid 10 liras and get another taxi paid 18 liras!!
4- Remember to ask always for a 'Fiche' (invoice in Turkish) to be able to track the driver if something is forgotten or lost in taxi or you meet a taxi-robber.
You can also take a photo of taxi numberplate when you want to get in and while using the trunk for putting your stroller (maybe you won't have the time or chance to do it when you want to get off)
5- always make change and have small notes of 5, 10, 20 and enough coins because some drivers prefer to keep the change without asking you :)