I'm going to assume you are fairly new to the game - if this isn't the case apologies if some of this seems very basic.

One thing about all three of the champions you mentioned is they are all melee (Zed and Kat have ranged abilities but will still generally look to all in at close range).

When you play mid vs a melee champ as someone with range like Ahri, Jayce or even fiddle, make sure you punish them for this accordingly, do not let them auto attack the wave for free at melee range, as ahri throw your Q + autos in their face, as Jayce EQ them into oblivion and punish with W's.

The only way they should be able to push you in is if you either, a) let them, or b) take a bad trade to the point where you can't go near the wave anymore.

The main mistake newer players make is being scared when they take damage and backing off, for example if Kat EQW's you for a chunk of your health do not back off, she has no cooldowns left! Return as much damage as you can and make her think twice about doing that again. Obviously there are other issues here like mana management etc. vs resourceless champs like Kat and Zed but try and keep these general principles in mind and you should find these matchups easier.

The only one of those champions that is something of a lane bully is Zed, Kat wins lanes by buying a lot of sustain and withering you down over time until she can all in at level six or by roaming the map and getting kills/resets, and Vi generally isn't even played as a laner.

Ahri in particular should demolish all of those matchups - you will be able to outpoke all those champions, push the wave harder than them, and prevent any all ins. (This depends on you playing the matchup correctly but when Kat looks to all in she's standing still during death lotus - that's a free E+Q+W combo, and you can stop a good chunk of the damage, when Zed ults he appears behind you every time, so if you time it properly that's a free charm + QW too. If you struggle with this you can always just spirit rush away too.)