This function takes a string input and performs the following operations: increments uppercase alphabets by 1, keeps all non-alphabet characters, and removes any numbers present in the input string.

[CODE]:
```python
def approx_function(input_str):
    result = ""
    for char in input_str:
        if char.isalpha():
            if char.isupper():
                result += chr(((ord(char) - 65 + 1) % 26) + 65)
            else:
                result += char
        elif not char.isdigit():
            result += char
    return result
```