The function takes a string input and returns a new string where each character is replaced by the character 15 positions ahead of it in the alphabet, wrapping around if necessary.

[CODE]: 
```python
def approx_function(s):
    result = ""
    for c in s:
        if c.isalpha():
            new_c = chr(((ord(c) - ord('a') + 15) % 26) + ord('a'))
            result += new_c
        else:
            result += c
    return result
```