Antonyms of verb despair

1 sense of despair

Sense 1
despair -- (abandon hope; give up hope; lose heart; "Don't despair--help is on the way!")
       Antonym of hope (Sense 2)
      => hope -- (be optimistic; be full of hope; have hopes; "I am still hoping that all will turn out well")

Synonyms/Hypernyms (Ordered by Estimated Frequency) of verb despair

1 sense of despair

Sense 1
despair -- (abandon hope; give up hope; lose heart; "Don't despair--help is on the way!")

Antonyms of adj despairing

1 sense of despairing

Sense 1
despairing, desperate -- (arising from or marked by despair or loss of hope; "a despairing view of the world situation"; "the last despairing plea of the condemned criminal"; "a desperate cry for help"; "helpless and desperate--as if at the end of his tether"; "her desperate screams")

INDIRECT (VIA hopeless) -> hopeful -- (having or manifesting hope; "a line of people hopeful of obtaining tickets"; "found a hopeful way of attacking the problem")

Similarity of adj despairing

1 sense of despairing

Sense 1
despairing, desperate -- (arising from or marked by despair or loss of hope; "a despairing view of the world situation"; "the last despairing plea of the condemned criminal"; "a desperate cry for help"; "helpless and desperate--as if at the end of his tether"; "her desperate screams")
       => hopeless (vs. hopeful) -- (without hope because there seems to be no possibility of comfort or success; "in an agony of hopeless grief"; "with a hopeless sigh he sat down")