These are folding fans called sensu. They are easily carried in a purse or bag. It is not unusual to see people use them on the train. When wearing a kimono, fans are placed in front between you and the obi, the wide sash worn at the waist.
One of my Japanese students gave me the purple and white fan on the left over 20 years ago . It still has a nice scent. I believe it is an expensive, well-made fan. When I first came to Japan, fans were pretty expensive. Now, fans vary in quality and price. The one with the blue and white wave pattern came from the 100 yen shop. Its blue cover was bought separately. The yellow monkey fan was bought many years ago for my daughter long. It was bought before there were 100 yen shops.
A little American girl once showed me how to fold the purple and white fan after I received it. She folded it carefully one fold at a time. She knew what she was doing. When cared for properly, a fan can last a very long time.