Map functions over array with Postgres
If you are merely looking to increment each element of an input array, this simple function is one method of doing it.

CREATE OR REPLACE FUNCTION add1 (int[]) RETURNS int[] AS
$func$
DECLARE
    e       int;
    new_arr int[] := '{}';
BEGIN
    FOREACH e IN ARRAY $1 LOOP
        e := e + 1;
        new_arr := new_arr || e;
    END LOOP;
    RETURN new_arr;
END;
$func$ LANGUAGE plpgsql STABLE;

SELECT add1(array[1,5,8,15]::int[]);
    add1
------------
 {2,6,9,16}


Or queried from your table

select id, array_col, add1(array_col) from yourtable;
 id |      arr      |     add1
----+---------------+---------------
  1 | {1,3,6,9}     | {2,4,7,10}
  2 | {10,20,30,40} | {11,21,31,41}


Plain SQL version of the function:

CREATE OR REPLACE FUNCTION add1(int[]) RETURNS int[] AS
$func$
    SELECT array_agg(vals)
    FROM (select unnest($1) + 1 as vals) AS x;
$func$ LANGUAGE sql STABLE;