Fixed point theory and some of its applications in intuitionistic fuzzy normed spaces

Coupled fixed point theorems have an important role in the fixed point theory and are used to show existence and uniqueness of solution of periodic boundary value problem in applied mathematics. In this thesis, firstly, for an arbitrary positive integer it was given the concepts of n ‐tuplet fixed point and n ‐tuplet coincidence point which are the generalization of coupled fixed point and coupled coincidence point. Theorems related with existence and uniqueness of these concepts in partially ordered complete metric space were proven. After, n ‐tuplet fixed point theorems were studied in partially ordered complete intuitionistic fuzzy normed space. Also, approximate fixed point property of a function and a set was defined in intuitionistic fuzzy normed space. Intuitionistic fuzzy version of class of maps used in fixed point theory was given and it was researched whether these maps have approximate fixed point property or not. Keywords: n ‐tuplet fixed point, n ‐tuplet coincidence point, intuitionistic fuzzy normed space, intuitionistic fuzzy approximate fixed point property