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Fixed points for set and single valued maps without continuity

Djoudi A., Khemis R.

Demonstratio Mathematica

2005

Vol. 38, nr 3

739-751

In this paper we prove some common fixed point theorems for single valued and set valued mappings on a metric space. The theorems use minimal type commutativity and strict contractivity conditions with no continuity requirements. The theorems extend previous results on delta-compatible and continuous maps of [1] and [11] to a wider class of weakly compatible mappings not necessarly continuous. Also, a common fixed point theorem which applies to a sequence of set valued mappings is given.