Fixed Point Theorems in Partially Ordered Metric Spaces and Existence Results for Integral Equations

Abstract

We derive some new coincidence and common fixed point theorems for self-mappings satisfying a generalized contractive condition in partially ordered metric spaces. As applications of the presented theorems, we obtain fixed point results for generalized contraction of integral type and we prove an existence theorem for solutions of a system of integral equations.

Keywords:

• Fixed point
• Integral equations
• Ordered metric space

AMS Subject Classification:

• 54H25
• 47H10

ACKNOWLEDGMENTS

All authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript. C. Vetrois supported by University of Palermo, Local University Project R. S. ex 60.