Critical point results and their applications

Abstract

The purpose of this paper is to study the concept of a critical point in complete cone metric spaces and its application in Ekeland type variational principle. For this, we consider the concept of a ?-space, which is weaker than a cone metric space in general. Actually, we rectify some critical point results in ?-spaces, and complete cone metric spaces. Indeed, we try to correct some gaps in some definitions and main results of the previous works and apply them in the set valued case. Moreover, we give an improved version of Ekeland type variational principle in complete cone metric spaces.