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 (fx, fy) ≤ 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. [ABSTRACT FROM AUTHOR]