'Remember' in the Bible

Then she said, "Please may the king remember Yahweh your God, {to prevent the increase of blood avengers who kill}, [so that they] not wipe out my son." He said, "{As Yahweh lives}, surely not one hair shall fall from your son to the ground."

(Now Absalom had taken and set up for himself in his lifetime a stone pillar that [is] in the valley of the king, because he said, "I have no son in order to remember my name," and he called the stone pillar by his name. It [is] called the monument of Absalom until this day).

and he said to the king, "May not my lord hold me guilty, and may you not remember how your servant did wrong on the day that my lord the king went out from Jerusalem, by taking it to heart!