Old fixtures it may be possible to replace the socket. You will have to disassemble the fixture enough to get the socket out, then see if it matches one from HD/lowes/amazon, and replace it. I assume it's e26 and not e12? (hard to tell from the pictures.)

E12 (I did this recently on an outdoor fixture I didn't want to replace)

https://www.homedepot.com/p/Commercial-Electric-Keyless-Socket-2-Pack-81605/306197919

E26

https://www.homedepot.com/p/Commercial-Electric-Porcelain-Socket-81615/306198159

https://www.amazon.com/Creative-Hobbies-ELT5561A-Incandescent-One-Piece/dp/B00X4C403O