The function shifts lowercase alphabetic characters in the input string by 22 positions forward in the alphabet while wrapping around and converts uppercase alphabetic characters to their lowercase equivalents. Numeric and non-alphabetic characters remain unchanged.

[CODE]: 
```python
def approximate_function(input_str):
    result_str = ""
    for char in input_str:
        if char.isupper():
            result_str += char.lower()
        elif char.islower():
            result_str += chr(((ord(char) - ord('a') + 22) % 26) + ord('a'))
        else:
            result_str += char
    return result_str
```