Search in JSON api url with ajax

I have an api URL it's output JSON, it is about daily deals like groupon.

I want to create a search form and client search in this json

Samle json url here

I'm decode JSON like that and show it but how to search in this api url i don't know.

$param = array(
    'apiKey' => 'VN43ZG2LLHKHHIU6',
    'publisherId' => 316,
    //'isPopular' => 'on',
    'p' => $sayfasi,
    'itemInPage' => $sayi
);

if(isset($tagid) && $tagid !='')
    $param['tagIds[]'] = $tagid;

if(isset($cityId) && $cityId !='')
    $param['cityId'] = $cityId;



$jsonurl     = 'http://ift.tt/1YHObtK?'.http_build_query($param);


//$json        = CurlConnect($jsonurl

$json = file_get_contents($jsonurl);

$json_output = json_decode($json);

Search form should search in deals: title, description

Sample deals json block

"deals":[  
      {  
         "id":"1041296",
         "title":"Tüm Cinemaximum'larda İndirimli Sinema Biletleri 9.50 TL'den Başlayan Fiyatlarla!",
         "description":"Cinemaximum İndirimli Bilet Fırsatı\r\nCinemaximum'larda indirimli bilet fırsatını kaçırmayın. ",
         "howToUse":null,
         "endDate":"2015-12-26 23:59:59",
         "discountPercent":"41",
         "country":"Turkey",
         "businessIds":"",
         "latLngs":"",
         "city":"",
         "provider":"Fırsat Bu Fırsat",
         "realPriceWithSymbol":"16 TL",
         "dealPriceWithSymbol":"9.50 TL",
         "showDealUrl":"http://ift.tt/1mFkFsR",
         "buyDealUrl":"http://ift.tt/1YHObtM",
         "image200_H":"http://ift.tt/1mFkDBa",
         "timeLeft":43377
      },...

Click here view more answers http://ift.tt/1Oesz6K