ucfirst() function for multibyte character encodings

There is no mb_ucfirst function, as you've already noticed. You can fake a mb_ucfirst with two mb_substr:

function mb_ucfirst($string, $encoding)
{
    $firstChar = mb_substr($string, 0, 1, $encoding);
    $then = mb_substr($string, 1, null, $encoding);
    return mb_strtoupper($firstChar, $encoding) . $then;
}

as of 2019-11-18, it seems nobody on stackoverflow got this right, here's how mb_ucfirst() should be implemented in userland:

function mb_ucfirst(string $str, string $encoding = null): string
{
    if ($encoding === null) {
        $encoding = mb_internal_encoding();
    }
    return mb_strtoupper(mb_substr($str, 0, 1, $encoding), $encoding) . mb_substr($str, 1, null, $encoding);
}

function mb_ucfirst($string)
{
    return mb_strtoupper(mb_substr($string, 0, 1)).mb_substr($string, 1);
}

This is more concise solution, although it is rather similar to ucwords function:

$final_string = mb_convert_case($your_string, MB_CASE_TITLE, 'UTF-8');

If you need to capitalize string consist of one word, it is the best solution.