Hicks’ contraction principle

T. Hicks in [128] considered another notion of probabilistic contraction mapping than probabilistic q-contraction, which is incomparable with probabilistic q-contraction, [262]. In section 5.1 two types of generalizations of Hick’s notion of C-contraction is introduced and some fixed point theorems for these new classes of mappings are proved. A multi-valued generalization of the notion of C-contraction is given in section 5.2 and two fixed point theorems for multi-valued mappings are proved, where some results on infinitary operations from section 1.8 are used.