My Melrose Pepper plant's leaves are starting to curl and shrivel. I've inspected the leaves and see no signs of insects. The plant is just starting to bear fruit. Can you tell me what I should do?
Thanks in advance for your help.

That looks like thrip or aphid damage. But if you aren't finding any sucky bugs, you may want to do some reading on pepper plant diseases. Mosaic comes to mind.

Did you maybe use too much fertilizer? If so water them a lot.

With it localized to the newer leaves and not the 'adult' leaves, that makes me think bugs. Aphids are hard to see and come in 8 billion different forms, including a VERY annoying ROOT aphid that you will never see above ground.

Maybe try some neem and see if it helps, or use a damp rag to wipe the underside of the leaves off.