Existence and uniqueness of fixed point for mixed monotone ternary operators with application

摘要

In this paper, partial order theory is used to study the fixed point of a mixed monotone ternary operator A : P × P × P → P . The existence and uniqueness of a fixed point are obtained without assuming the operators to be compact or continuous. In the end, the application to an integral equation is presented. Our results unify, generalize, and complement various known comparable results from the current literature. MSC:47H05, 47H10.