Can a specific performance be in the form of liquidated damages mentioned in the contract?

Specific performance is the notion that a party can be compelled to act or refrain from acting, as the case may be.  Generally, injunctive relief is only available when there is no adequate remedy at law.  So, it is usually in place of actual damages.  However, if the contract allows for both, the court should enforce both.  Liquidated damages usually exist when the parties agree to a sum certain rather than calculating what the actual damages will be. I trust this answers your question, but, if you are near to me, feel free to call or e-mail on a free initial basis.