Stripping an extension and directories from a string?

say I have the sring

my/file/file.txt

How would I go about stripping the slashes and the extension to just file? I have google'd my problem, and people have suggested basename, but I'm looking for something that would work on Windows too, any ideas?

Here's what I've tried:

char *rm_ext(char *file) {
    char *retstr;
    char *lastdot;
    if (file == NULL)
         return NULL;
    if ((retstr = malloc (strlen (file) + 1)) == NULL)
        return NULL;
    strcpy (retstr, file);
    lastdot = strrchr (retstr, '.');
    if (lastdot != NULL)
        *lastdot = '\0';
    return retstr;
}

char *get_file_name(char *path) {
    char *s = strrchr(path, '/');
    if (!s) return rm_ext(strdup(path));
    char *res = strdup(s + 1);
    char *res_no_ext = rm_ext(result);
    return res_no_ext;
}

It works, but not with D:/ or double slashes, also I think it's giving me memory leaks since there's a bunch of hidden mallocs from strdup.