MySQL - Capitalize first letter of each word including Turkish Characters

Question

I have mysql function that capitalizes the first letter of each word in desired string.

What I want to do is to convert Turkish characters to Turkish occurence instead of English occurence such as;

i = I (should be İ), ş = S (should be Ş) etc.

Correct conversion table;

i = İ (currently : I)
ö = Ö (currently : O)
ü = Ü (currently : U)
ç = Ç (currently : C)
ş = Ş (currently : S)

I tested with both utf8 and utf8_turkish_ci encoding but same result.

Used function is;

CREATE FUNCTION CAP_FIRST (input VARCHAR(255))

RETURNS VARCHAR(255)

DETERMINISTIC

BEGIN
    DECLARE len INT;
    DECLARE i INT;

    SET len   = CHAR_LENGTH(input);
    SET input = LOWER(input);
    SET i = 0;

    WHILE (i < len) DO
        IF (MID(input,i,1) = ' ' OR i = 0) THEN
            IF (i < len) THEN
                SET input = CONCAT(
                    LEFT(input,i),
                    UPPER(MID(input,i + 1,1)),
                    RIGHT(input,len - i - 1)
                );
            END IF;
        END IF;
        SET i = i + 1;
    END WHILE;

    RETURN input;
END;

How could I solve this issue with pure mysql function?