Integral type contractions in partial metric spaces

It is known that history of mathematics is old as history of humanity. Mathematics covered a distance significantly from ancient age to now. Recently, there are many important works for modern mathematics([6],[8]). Let X be a nonempty set and f : X ? X be a mapping. If f (x) = x, for some x ? X, then x is fixed point of f . Banach fixed point theorem was introduced in 1922 in complete metric spaces as “(X, d) be a complete metric space and f : X ? X be a self-mapping. If there exists 0 ? k < 1 such that d (f x, f y) ? kd (x, y) for all x, y ? X. Then f has unique fixed point”([1]). Partial metric spaces were introduced by Matthews (1994) as a generalisation of usual metric spaces where the self distance for any point need not be equal to zero. In this work, we define generalized integral type F?contractions and prove common fixed point theorems for four mappings satisfying these types contractions in partial metric spaces.