Yes.  The standard for Mobile WiMAX or IEEE 802.16e was finalized late in 2005. 

Increasingly, it appears that the 802.16e mobile WiMAX standard is the version that the majority of operators are moving towards.  While it is premature to say that the 802.16d version is likely to wither away, most vendors, even those busily shipping Fixed WiMAX radios, have upgrade procedures in place for customers to switch.

The 802.16e Mobile WiMAX standard can competently support fixed broadband applications as well as mobile.  The jury is a bit out as to how well that can be done on a homogenous mobile/fixed needs network as the types of customers served are a bit different.  In general, customers utilizing a Fixed WiMAX service are more often businesses with much higher bandwidth and IP-based service needs.  Clearly, hybrid networks may make a lot more sense in the short run for many service providers.  The most recent feedback from carriers is that they feel truly mobile capability even for most business customers has enormous marketing power and expectations are that mobility will predominate.  Clearly for US carriers, which largely means Clearwire, mobile applications are the future.