The purpose of this paper is to present, in the context of an ordered metric space, some fixed point theorems for continuous, nondecreasing mappings which satisfy Caristi type conditions with perturbed metrics. For example, the following theorem is proved.
Theorem 2.1. Let be a partially ordered set and suppose that there exists a metric in such that is a complete metric space. Let be a continuous and nondecreasing mapping such that
where are some altering distance functions. If there exists with , then has a fixed point in .
As an application, an existence result for a first-order periodic problem for a differential equation is given.