// Getting list items based on ODATA Query
function getListItems(url, listname, query, complete, failure) {

    // Executing our colors ajax request
    $.ajax({
        url: url + "/_api/web/lists/getbytitle('" + listname + "')/items" + query,
        method: "GET",
        headers: { "Accept": "application/json; odata=verbose" },
        success: function (data) {
            complete(data); // Returns JSON collection of the results
        },
        error: function (data) {
            failure(data);
        }
    });

}

$filter=AuthorId eq <UserId>

function getCurrentUser(url,complete, failure)
{
    $.ajax({
        url: url + "/_api/web/currentUser",
        method: "GET",
        headers: { "Accept": "application/json; odata=verbose" },
        success: function (data) {
            complete(data.d);
        },
        error: function (data) {
            failure(data);
        }
    });
}

function getMyListItems(url, listname,complete, failure) {
  getCurrentUser(url,
    function(user){
       var query = '?$filter=AuthorId eq ' + user.Id;
       getListItems(url,listname,query,complete,failure);
    },
    failure
  );
}

$.ajax(
        {
            url: url,
            type: "GET",
            contentType: "application/json;odata=verbose",
            headers: { "Accept": "application/json;odata=verbose" },

            success: function (data) {
            var result = data.d.results;

                for (var i = 0; i < result.length; i++) {

    alert(result[i].FirstName);
            alert(result[i].LastName);
                  }
         }

        error: function (err) {
                alert(JSON.stringify(err));
            }