A note on the fixed point theorem of Gornicki

摘要

In this note, we show that the main result (Theorem 2.6) due to Gornicki (J Fixed Point Theory Appl 21:29, 2019. 10.1007/s11784-019-0668-0) is still valid if we replace the assumption of continuity of the mapping by some weaker versions of continuity conditions. As a by-product, we provide few more new answers to the open question of Rhoades (Contemp Math 72:233-245, 1988).