Is it permissible for a client to ask an Islamic bank to discount part of the price of a commodity in case of early settlement, and is the bank's dealing in this manner similar to usurious banks?

Discounting part of a deferred debt in exchange for its early payment is impermissible according to the majority of scholars, including the four Madhhabs. This is known by the rule of "Dha' wa Ta'ajjal" (forgive [part of the debt] and hasten [payment]). A group of scholars, however, deemed it permissible, and this is a narration from Ahmad and the choice of Ibn Taymiyyah and Ibn al-Qayyim. If a creditor waives part of a debt for the debtor in exchange for expedited payment, without prior collusion or stipulation, there is no harm in it. As for Islamic banks that deal in this manner, they are not described as usurious, because they are based on dealing according to the regulations of Islamic Sharia (definition).