Postgres 9.5

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CREATE TABLE groups ( name VARCHAR, grp JSONB);
 INSERT INTO groups (name, grp) VALUES 
 ('joe', '[{"gid": "1", "ona": "joe", "tit": "group 1 "}, {"gid": "2", "ona": "harry", "tit": "tester1 group 2"}, {"gid": "3", "ona": "moe", "tit": "group 3"}]'),
 ('harry', '[{"gid": "1", "ona": "joe", "tit": "group 1 "}, {"gid": "2", "ona": "harry", "tit": "tester1 group 2"}, {"gid": "3", "ona": "moe", "tit": "group 3"}]'),
 ('moe' , '[{"gid": "1", "ona": "joel", "tit": "group 1 "}, {"gid": "2", "ona": "harry", "tit": "tester1 group 2"}, {"gid": "3", "ona": "moe", "tit": "group 3"}]')
 
INSERT 0 3

UPDATE groups AS g
   SET grp = REPLACE(grp::text, '"tit": "group 1 "','"tit": "newTitle Group 1 "')::json
 WHERE g.name IN ( SELECT g.name 
                     FROM groups AS g 
                    CROSS JOIN jsonb_array_elements(grp) AS j 
                    WHERE j.value->>'ona' = 'joe' ) 
  
UPDATE 2

SELECT *
  FROM groups
  
name
grp

moe
[{"gid": "1", "ona": "joel", "tit": "group 1 "}, {"gid": "2", "ona": "harry", "tit": "tester1 group 2"}, {"gid": "3", "ona": "moe", "tit": "group 3"}]

joe
[{"gid": "1", "ona": "joe", "tit": "newTitle Group 1 "}, {"gid": "2", "ona": "harry", "tit": "tester1 group 2"}, {"gid": "3", "ona": "moe", "tit": "group 3"}]

harry
[{"gid": "1", "ona": "joe", "tit": "newTitle Group 1 "}, {"gid": "2", "ona": "harry", "tit": "tester1 group 2"}, {"gid": "3", "ona": "moe", "tit": "group 3"}]

SELECT 3

name	grp
moe	[{"gid": "1", "ona": "joel", "tit": "group 1 "}, {"gid": "2", "ona": "harry", "tit": "tester1 group 2"}, {"gid": "3", "ona": "moe", "tit": "group 3"}]
joe	[{"gid": "1", "ona": "joe", "tit": "newTitle Group 1 "}, {"gid": "2", "ona": "harry", "tit": "tester1 group 2"}, {"gid": "3", "ona": "moe", "tit": "group 3"}]
harry	[{"gid": "1", "ona": "joe", "tit": "newTitle Group 1 "}, {"gid": "2", "ona": "harry", "tit": "tester1 group 2"}, {"gid": "3", "ona": "moe", "tit": "group 3"}]