Handling dynamic aspect of databases and multiple support threshold requirement of items are two important challenges of frequent itemset mining algorithms. Frequent itemsets should be updated when the database is updated without re-running the mining algorithm. Frequent itemset mining algorithm should consider different support thresholds in order not to cause rare item problem. Existing dynamic itemset mining algorithms are devised for single support threshold whereas multiple support threshold algorithms are static. This thesis focuses on dynamic update problem of frequent itemsets under multiple support thresholds and introduces Dynamic MIS1 and Dynamic MIS2 algorithms. They are i) tree based and scan the database once, ii) consider multiple support thresholds, and iii) handle increments of additions, additions with new items and deletions. Proposed algorithms are compared to CFP-Growth++ and findings are; in static databases 1) Dynamic MIS1 achieves up to 5 times speed-up against CFP-Growth++ since it does not require tree pruning and merging, 2) execution time of Dynamic MIS2 and CFP-Growth++ are similar, 3) memory usage of Dynamic MIS1 is higher than CFP-Growth++, since it keeps whole tree in memory, in dynamic database 1) Dynamic MIS1 and Dynamic MIS2 perform better than CFP-Growth++ since they run only on increments, 2) Dynamic MIS1 can achieve speed-up of 56 times against CFP-Growth++, whereas the speed-up of Dynamic MIS2 cannot exceed 2 times, 3) Dynamic MIS2 is slightly better than CFP-Growth++ until increment size is less than 85% when the database is large and sparse, 25% when the database is small and dense.