converts wrongly (as i to I and vice versa).
The i you have entered is U+0069 (“LATIN SMALL LETTER I”, also ASCII 105) and is always defined as lowercase. The I you have entered is U+0049 (“LATIN CAPITAL LETTER I”, also ASCII 73), and is always defined as uppercase. As far as I know, it is always correct for a case conversion process to convert one to the other (as they are an upper/lower pair in the latin-based alphabets, as far as I understand it).
The İ is U+0130 (“LATIN CAPITAL LETTER I WITH DOT ABOVE”), and that one is considered uppercase/capital in Unicode definition; the ı is U+0131 (“LATIN SMALL LETTER DOTLESS I”) and is considered lowercase/small in Unicode. However, I am not an expert on the capitalization/lowercasization (not a word, I know) rules for the non-ASCII characters, so I don’t know if Unicode defines pairs for the case-conversion on those characters or not.
If you find official Unicode documentation that explains the rules for case conversion on those U+0130 and U+0131 characters (or that gives an exception for circumstances when U+0049 and U+0068 are not a pair with each other), then you can read the feature request/bug report FAQ and follow the instructions there on where to put in official feature requests / bug reports. In your official bug report, you will need to request that the development team improve the case-conversion features, and you will need to provide that reference to the developers, and explain the “correct behavior” as you understand it).
(Aside: I moved your topic from Plugins Development to Help Wanted, because it was not a plugin question.)