A common fixed point theorem of S.L. and S.P. Singh is generalized by weakening commutativity hypotheses and by increasing the number of functions involved.

/pdf/compatible-mappings-and-common-fixed-points-117iccel17.pdf

Compatible mappings and common fixed points

Formally we have arrived at the middle of the book. So you may need a pause for recovering, a pause which we want to fill up by some fixed point theorems supplementing those which you already met or which you will meet in later chapters. The first group of results centres around Banach’s fixed point theorem. The latter is certainly a nice result since it contains only one simple condition on the map F, since it is so easy to prove and since it nevertheless allows a variety of applications. Therefore it is not astonishing that many mathematicians have been attracted by the question to which extent the conditions on F and the space Ω can be changed so that one still gets the existence of a unique or of at least one fixed point. The number of results produced this way is still finite, but of a statistical magnitude, suggesting at a first glance that only a random sample can be covered by a chapter or even a book of the present size. Fortunately (or unfortunately?) most of the modifications have not found applications up to now, so that there is no reason to write a cookery book about conditions but to write at least a short outline of some ideas indicating that this field can be as interesting as other chapters. A systematic account of more recent ideas and examples in fixed point theory should however be written by one of the true experts. Strange as it is, such a book does not seem to exist though so many people are puzzling out so many results.

Fixed Point Theory

Some new common fixed point theorems under strict contractive conditions

Common fixed point results for noncommuting mappings without continuity in cone metric spaces

Common fixed points for maps on cone metric space

Commuting Mappings and Fixed Points

Common fixed points for noncontinuous nonself maps on nonmetric spaces

We obtain two fixed point theorems for a class of operators called occasionally weakly compatible maps defined on a symmetric space . These results establish two of the most general fixed point theorems for four maps.

http://www.math.ubbcluj.ro/~nodeacj/download.php?f=062rhoadesABS.pdf

Gerald Jungck

Papers

Compatible mappings and common fixed points

Commuting Mappings and Fixed Points

Common fixed point results for noncommuting mappings without continuity in cone metric spaces

Common fixed points for noncontinuous nonself maps on nonmetric spaces

Fixed point theorems for occasionally weakly compatible mappings