Sorry, it is very late so I may not explain all the details, but I have been working on this and I cannot understand why the object Item object reference in the array does not use the equals method of the Item class that it was given. I checked the class type of both Item objects inside the function and they return class Item.
import java.util.Arrays;
class Item{
    private int data;
    Item(int data){
        this.data=data;
    }
    public boolean equals(Item item){
        return data==item.data;
    }
    public String toString(){
        return String.format("{data: %d}", data);
    }
}
public class Problem3{
    public static void main(String[] args){
        Object object=new Object(){ public String toString(){return String.format("{hash code: %d}", hashCode());} };
        String date="Friday, July 29";
        Item item=new Item(2);
        Object[] array={"Fri, Jul 29", new Item(2), object, new Integer[]{212, 220, 240, 313, 316, 320, 323, 331}, new Double[]{Math.E, Math.PI, 9.80665}, new Boolean[]{true, true, true, true}, new String[]{"Eckhart", "Eric", "Owen", "Chris", "David", "Mark"}};
        System.out.println(Arrays.deepToString(array));
        System.out.println();
        System.out.println("Searching array for entries . . .");
        System.out.printf("\"%s\":  %b\n", date, isMember(array, date));
        System.out.printf("%s:  %b\n", item, isMember(array, item));
        System.out.printf("%s:  %b\n", object, isMember(array, object));
        System.out.print("[\u0065, \u03c0, \u0047]:  "+isMember(array, new Double[]{Math.E, Math.PI, 9.80665})); //\ud835 \u0065
    }
    private static boolean isMember(Object[] array, Object value){
        if(array.length>0){
            Object member=array[array.length-1];
            if(member instanceof Object[] && value instanceof Object[]){
                if(Arrays.deepEquals((Object[])member, (Object[])value)){
                    return true;
                }
            }
            else if(member.getClass().equals(Item.class) && value.getClass().equals(Item.class)){
                if(member.equals(value)){
                    return true;
                }
            }
            else if(member.equals(value)){ //Object parameter does not have field "data" of Item equals method, so "instance of Item" applied above
                return true;
            }
            Object[] arrayNext=Arrays.copyOf(array, array.length-1);
            return isMember(arrayNext, value);
        }
        return false;
    }
}
 
     
     
    