code: def test_fillna_dtype_conversion(self, using_infer_string):
      # make sure that fillna on an empty frame works
      df = DataFrame(index=["A", "B", "C"], columns=[1, 2, 3, 4, 5])
      result = df.dtypes
      expected = Series([np.dtype("object")] * 5, index=[1, 2, 3, 4, 5])
      tm.assert_series_equal(result, expected)
  
      msg = "Downcasting object dtype arrays"
      with tm.assert_produces_warning(FutureWarning, match=msg):
          result = df.fillna(1)
      expected = DataFrame(
          1, index=["A", "B", "C"], columns=[1, 2, 3, 4, 5]
      )
      tm.assert_frame_equal(result, expected)
  
      # empty block
      df = DataFrame(
          index=range(3), columns=["A", "B"], dtype="float64"
      )
      if using_infer_string:
          with tm.assert_produces_warning(
              FutureWarning, match="Downcasting"
          ):
              result = df.fillna("nan")
      else:
          result = df.fillna("nan")
      expected = DataFrame("nan", index=range(3), columns=["A", "B"])
      tm.assert_frame_equal(result, expected)
  
imports: import numpy
  import pytest
  from pandas._config import using_pyarrow_string_dtype
  from pandas import Categorical, DataFrame, DatetimeIndex, NaT, PeriodIndex, Series, TimedeltaIndex, Timestamp, date_range, to_datetime
  import pandas._testing
  from pandas.tests.frame.common import _check_mixed_float
label_desc: Use image node_id 18 for calling the TestFillNA obj's underlying member method code with example usage: obj.test_fillna_dtype_conversion(using_infer_string) without return types