A Generalization of Fixed-Point Theorems for Mappings with a Contractive Iterate

Abstract

In this paper, a generalization of fixed-point mappings with an iterate at a point in complete metric spaces is shown, using the notions of T-closed sets and i-P-regularity/d-P-regularity, proving conditions for the existence and uniqueness of the fixed point. Examples are provided to illustrate the results and an application to coupled fixed points is shown.

Keywords

• fixed point
• contractive iterate at a point
• coupled fixed point
• T-closed set