Coupled fixed point results for nonlinear integral equations

Abstract

In this paper, we prove some coupled coincidence point theorems for such nonlinear contraction mappings having a mixed monotone property in partially ordered metric spaces by dropping the condition of commutative. We also prove coupled common fixed point theorem for w-compatible mappings. An example of a nonlinear contraction mapping which is not applied by Lakshmikantham and Ćirić’s theorem [1] but applied by our result is given. Further, we apply our results to the existence theorem for solution of nonlinear integral equations.

Keywords

• Coupled fixed point
• Coupled coincidence point
• Coupled common fixed point
• Mixed monotone property
• Partially ordered set
• Integral equations