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fond‧ly

1 to believe something that is untrue, hope for something that will probably not happen etc :
Some people still fondly believe that modern science can solve all the world's problems.
fondly imagine/believe/hope etc
Some people still fondly believe that modern science can solve all the world's problems.2 in a way that shows you like someone very much [= lovingly]:
He turned to see her smiling fondly at him.
He turned to see her smiling fondly at him.