diff --git a/pandas/core/arrays/base.py b/pandas/core/arrays/base.py
index 7447d593a7ff0..4435d8b7c88ee 100644
--- a/pandas/core/arrays/base.py
+++ b/pandas/core/arrays/base.py
@@ -439,7 +439,7 @@ def isna(self) -> ArrayLike:
 
         Returns
         -------
-        na_values : Union[np.ndarray, ExtensionArray]
+        na_values : np.ndarray or ExtensionArray
             In most cases, this should return a NumPy ndarray. For
             exceptional cases like ``SparseArray``, where returning
             an ndarray would be expensive, an ExtensionArray may be
diff --git a/pandas/core/base.py b/pandas/core/base.py
index ee514888c6331..06b7cd9152fb7 100644
--- a/pandas/core/base.py
+++ b/pandas/core/base.py
@@ -4,11 +4,12 @@
 
 import builtins
 import textwrap
-from typing import Any, Dict, FrozenSet, List, Optional, Union
+from typing import Any, Dict, FrozenSet, Generic, List, Optional
 
 import numpy as np
 
 import pandas._libs.lib as lib
+from pandas._typing import ArrayLike
 from pandas.compat import PYPY
 from pandas.compat.numpy import function as nv
 from pandas.errors import AbstractMethodError
@@ -584,7 +585,7 @@ def _shallow_copy(self, obj, **kwargs):
         return self._constructor(obj, **kwargs)
 
 
-class IndexOpsMixin:
+class IndexOpsMixin(Generic[ArrayLike]):
     """
     Common ops mixin to support a unified interface / docs for Series / Index
     """
@@ -596,7 +597,7 @@ class IndexOpsMixin:
     )
 
     @property
-    def _values(self) -> Union[ExtensionArray, np.ndarray]:
+    def _values(self) -> ArrayLike:
         # must be defined here as a property for mypy
         raise AbstractMethodError(self)
 
@@ -1141,7 +1142,10 @@ def _map_values(self, mapper, na_action=None):
             values = self._values
             if na_action is not None:
                 raise NotImplementedError
-            map_f = lambda values, f: values.map(f)
+
+            def map_f(values, f):
+                return values.map(f)
+
         else:
             values = self.astype(object)._values
             if na_action == "ignore":
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 4bc5599297066..c0aab801a2024 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -13,7 +13,7 @@
 from pandas._libs.tslibs import OutOfBoundsDatetime, Timestamp
 from pandas._libs.tslibs.period import IncompatibleFrequency
 from pandas._libs.tslibs.timezones import tz_compare
-from pandas._typing import DtypeObj, Label
+from pandas._typing import ArrayLike, DtypeObj, Label
 from pandas.compat import set_function_name
 from pandas.compat.numpy import function as nv
 from pandas.util._decorators import Appender, Substitution, cache_readonly, doc
@@ -182,7 +182,7 @@ def _new_Index(cls, d):
     return cls.__new__(cls, **d)
 
 
-class Index(IndexOpsMixin, PandasObject):
+class Index(IndexOpsMixin[ArrayLike], PandasObject):
     """
     Immutable ndarray implementing an ordered, sliceable set. The basic object
     storing axis labels for all pandas objects.
@@ -254,7 +254,7 @@ def _outer_indexer(self, left, right):
         return libjoin.outer_join_indexer(left, right)
 
     _typ = "index"
-    _data: Union[ExtensionArray, np.ndarray]
+    _data: ArrayLike
     _id = None
     _name: Label = None
     # MultiIndex.levels previously allowed setting the index name. We
@@ -3805,7 +3805,7 @@ def array(self) -> ExtensionArray:
         return array
 
     @property
-    def _values(self) -> Union[ExtensionArray, np.ndarray]:
+    def _values(self) -> ArrayLike:
         """
         The best array representation.
 
diff --git a/pandas/tests/indexes/period/test_constructors.py b/pandas/tests/indexes/period/test_constructors.py
index 4ec7ef64e2272..56383826db164 100644
--- a/pandas/tests/indexes/period/test_constructors.py
+++ b/pandas/tests/indexes/period/test_constructors.py
@@ -321,7 +321,7 @@ def test_constructor_mixed(self):
     def test_constructor_simple_new(self):
         idx = period_range("2007-01", name="p", periods=2, freq="M")
 
-        with pytest.raises(AssertionError, match="<class .*PeriodIndex'>"):
+        with pytest.raises(AssertionError, match="PeriodIndex"):
             idx._simple_new(idx, name="p")
 
         result = idx._simple_new(idx._data, name="p")
@@ -339,7 +339,7 @@ def test_constructor_simple_new(self):
     def test_constructor_simple_new_empty(self):
         # GH13079
         idx = PeriodIndex([], freq="M", name="p")
-        with pytest.raises(AssertionError, match="<class .*PeriodIndex'>"):
+        with pytest.raises(AssertionError, match="PeriodIndex"):
             idx._simple_new(idx, name="p")
 
         result = idx._simple_new(idx._data, name="p")
diff --git a/pandas/tests/series/methods/test_argsort.py b/pandas/tests/series/methods/test_argsort.py
index 4353eb4c8cd64..53e5dbd87e508 100644
--- a/pandas/tests/series/methods/test_argsort.py
+++ b/pandas/tests/series/methods/test_argsort.py
@@ -53,7 +53,7 @@ def test_argsort_stable(self):
         tm.assert_series_equal(qindexer.astype(np.intp), Series(qexpected))
         msg = (
             r"ndarray Expected type <class 'numpy\.ndarray'>, "
-            r"found <class 'pandas\.core\.series\.Series'> instead"
+            r"found (<class ')?pandas\.core\.series\.Series('>)? instead"
         )
         with pytest.raises(AssertionError, match=msg):
             tm.assert_numpy_array_equal(qindexer, mindexer)