The use of fibre techniques plays the important role in topological fixed point theory and its applications.In this book, we introduce recent developments in Nielsen fixed point theory of fibre preserving map.There is well known addition formulae expressing the Nielsen number of the fibre preserving map as a simple sum of Nielsen numbers on the fibres.We generalize these ideas to the setting of fibre preserving maps defined locally.We first extend the product formula for the index of a fixed point class of a fibre preserving map to the setting of fibre preserving maps defined locally.Then, we...

Topological fixed point(coincidence) theory deals with the estimation of the number of fixed points(coincidences) of maps.In this book, we introduce recent developments in the epsilon Nielsen fixed point and coincidence theory of map.There is well known the epsilon Nielsen theory expressing the epsilon Nielsen number is a bigger than the usual Nielsen number. We generalize these ideas to the setting of coincidence two maps. We first extend the algebraic method of computing the epsilon Nielsen coincidence number. Then, we prove the problem of minimizing the number of the epsilon coincidence...