Is it possible to upgrade my laptop (an Acer Aspire 4730Z) which has a dual-core processor to use Core i3/i5/i7?
Short answer, No
Long answer, most notebooks are built with specific motherboards being used for that particular version. Unlike a desktop, the processors are sometimes soldered on, and in other cases, without disabling the whole unit, impossible to reach. Therefore it is rarely if ever viable to upgrade a notebook processor. However, there are certain model big brand notebooks that does support upgrading the processor, but you will have to look for them specifically. The 4730Z is a notebook that can have the processor upgrade, however, the following would be a problem:
As far as the jump from dual core to I series Intel chips are concerned, you have to replace the motherboard and memory to be able to do the upgrade, and on a laptop, buying a new one is a better option. The I series uses a different socket, as well as Dual or Triple Channel memory.