The function takes an input string and replaces the first character of the string with its adjacent character in the alphabets by incrementing its ASCII value by 1. If the first character is a non-alphabetic character (such as digits or special characters), the function returns the same character unchanged.

[CODE]: 

```python
def approx_function(input_str):
    if input_str[0].isalpha():
        next_char = chr(ord(input_str[0]) + 1)
        return next_char + input_str[1:]
    else:
        return input_str
```