Proceedings of the American Mathematical Society
Simeon Reich (1974) proved that the fixed point theorem for single-valued mappings proved by Boyd and Wong can be generalized to multivalued mappings which map points into compact sets. He then asked (1983) whether his theorem can be extended to multivalued mappings whose range consists of bounded closed sets. In this note, we provide an affirmative answer for a certain subclass of Boyd-Wong contractive mappings.
Original Publication Citation
Daffer, P. Z., Kaneko, H., & Li, W. (1996). On a conjecture of S. Reich. Proceedings of the American Mathematical Society, 124(10), 3159-3162. doi:10.1090/s0002-9939-96-03659-3
Daffer, Peter Z.; Kaneko, Hideaki; and Li, Wu, "On a Conjecture of S. Reich" (1996). Mathematics & Statistics Faculty Publications. 145.