I have a list of functions of the type:

func_list = [lambda x: function1(input),lambda x: function2(input),lambda x: function3(input),lambda x: x]

and an array of shape [4, 200, 200, 1] (a batch of images).

I want to apply the list of functions, in order, along the 0th axis.

EDIT: Rephrasing the problem. This is equivalent to the above. Say, instead of the array, I have a tuple of 4 identical arrays, of shape (200, 200, 1), and I want to apply function1 on the first element, function2 on the second element, etc. Can this be done without a for loop?

You can iterate over your function list using np.apply_along_axis:

import numpy as np
x = np.ranom.randn(100, 100)
for f in fun_list:x = np.apply_along_axis(f, 0, x)

Based on OP's Update

Assuming your functions and batches are the same in size:

batch = ... # tuple of 4 images  
batch_out = tuple([np.apply_along_axis(f, 0, x) for f, x in zip(fun_list, batch)])