Hungarian term (edited): (fellebbezés) tárgyaláson kívüli elbírálás(a)

A felek kérhetik a fellebbezés tárgyaláson kívül történő elbírálását. -
The parties may request that the appeal be reviewed without trial (proceedings).

fellebbezés : appeal
elbírálás (here) : review
tárgyalás : trial, trial proceedings

NB: elbírálás (to review, i.e. to evaluate) is not to be confused with ítélethozatal (to adjudicate)

Examples:

Appeal
Timely resort by an unsuccessful party in a lawsuit or administrative proceeding to an appropriate superior court empowered to review a final decision on the ground that it was based upon an erroneous application of law.
A person who initiates an appeal—the appellant, sometimes called the plaintiff in error, must file a notice of appeal, along with the necessary documents, to commence appellate review. The person against whom the appeal is brought, the appellee, then files a brief in response to the appellant's allegations.
http://legal-dictionary.thefreedictionary.com/appeal

2. MEANS OF CHANGING JUDGMENTS AND ORDERS
(a) Appeal
An appeal is available only for judgments or orders issued by the court following a full trial where both sides appeared and were heard. No new evidence may be presented in an appeal, it is a request to a have a higher court review the trial on the basis that the trial court made mistakes that would affect the outcome. Such mistakes could be a mistake in deciding a fact or in applying the law. The procedure for appeals is rather complex, and different rules apply for each of the four judicial departments.
http://www.jdbar.com/Articles/changing-orders.html

Appealing or Modifying Your Final Divorce Decree -
...The appellate court, usually made up of 3 judges, reviews your appeal and all of its supporting documents. Unlike the trial court, they do not consider new evidence or hear testimony of the parties or witnesses.
http://www.equalityinmarriage.org/adappeal.html

What is an appeal?
An appeal is a review by a higher court of a lower court to determine if the lower court made a legal mistake. An appeal is not a new trial or a chance to introduce new evidence.
http://divorcesupport.about.com/od/yourlegalrights/a/appeal_...

Appeals without trial proceedings -
...cases are often resolved when the court grants a motion for summary judgment. Fortunately for the appellant, the court of appeal will not review the matter with automatic deference to the summary judgment ruling under the substantial evidence standard of review. On the contrary, the trial court will review the judgment under the de novo standard of review.
http://www.kassounilaw.com/appeals/appeal-without-trial-proc...