Ok, thank you guys for your efforts, it seems like I found the solution. Apparently DECLARE has to be in the block (BEGIN-END), and also had to change the way to handle SQLSTATE '02000'.
DELIMITER
CREATE PROCEDURE emel (IN alapag VARCHAR(45))
BEGIN
DECLARE aaa VARCHAR(45);
DECLARE atEnd SMALLINT DEFAULT 0;
DECLARE notFound CONDITION FOR SQLSTATE '02000';
DECLARE c CURSOR FOR (SELECT nev FROM alapanyag);
DECLARE CONTINUE HANDLER FOR notFound
SET atEnd = 1;
OPEN c;
thisLoop:LOOP
FETCH c INTO aaa;
IF atEnd<>0 THEN
LEAVE thisLoop;
END IF;
IF aaa LIKE alapag THEN
UPDATE alapanyag
SET egysegar=egysegar*1.5;
END IF;
END LOOP;
CLOSE c;
END
DELIMITER ;