BUG Fix: pd.apply returns a dataframe when empty dataframe instead of a series

doc/source/whatsnew/v1.5.0.rst

@@ -795,6 +795,7 @@ Conversion
 - Bug in metaclass of generic abstract dtypes causing :meth:`DataFrame.apply` and :meth:`Series.apply` to raise for the built-in function ``type`` (:issue:`46684`)
 - Bug in :meth:`DataFrame.to_records` returning inconsistent numpy types if the index was a :class:`MultiIndex` (:issue:`47263`)
 - Bug in :meth:`DataFrame.to_dict` for ``orient="list"`` or ``orient="index"`` was not returning native types (:issue:`46751`)
+- Bug in :meth:`DataFrame.apply` returns a dataframe when empty dataframe instead of a series (:issue:`39111`)
 
 Strings
 ^^^^^^^

pandas/core/apply.py

@@ -790,7 +790,10 @@ def apply_empty_result(self):
 
         if not should_reduce:
             try:
-                r = self.f(Series([], dtype=np.float64))
+                if self.axis == 0:
+                    r = self.f(Series([], dtype=np.float64))
+                else:
+                    r = self.f(Series(index=self.columns, dtype=np.float64))
             except Exception:
                 pass
             else:

pandas/tests/apply/test_frame_apply.py

@@ -1577,3 +1577,11 @@ def test_apply_type():
     result = df.apply(type, axis=1)
     expected = Series({"a": Series, "b": Series, "c": Series})
     tm.assert_series_equal(result, expected)
+
+
+def test_apply_on_empty_dataframe():
+    # GH 39111
+    df = DataFrame({"a": [1, 2], "b": [3, 0]})
+    result = df.head(0).apply(lambda x: max(x["a"], x["b"]), axis=1)
+    expected = Series([])
+    tm.assert_series_equal(result, expected)