Fixed Points on Probabilistic and Fuzzy Structures

In this book, we introduce some
generalized probabilistic structure by extending several
concepts of known classical spaces such as Random Space,
Ultrametric Space and Hyper Space. In these newly developed
probabilistic structure, we prove several fixed point
theorem under some generalized contraction conditions.
Particularly, a fixed point theorem for iterated function
system (IFS) on a precompact probabilistic metric (PM)
spaces investigated. In addition, we extend the theory of
fixed points for multi-valued contractions in PM spaces and
prove several common fixed point theorems and coincidence
point theorems. In the case of non existence of fixed point,
we study the approximate fixed point with some weak
conditions. In chapter 6 we prove a fixed point theorem for
self discontinuious mappings on probabilistic normed
spaces.Finally, in the last two chapters, we considered the
intuitionistic fuzzy metric spaces. We extend the fuzzy
quasi-metric spaces to intuitionistic fuzzy quasi-metric
spaces. By defining an appropriate contraction condition we
proved a fixed point theorem in this space.