Stability of tripled fixed point iteration procedures for mixed monotone mappings

Abstract

Recently, Berinde and Borcut [Berinde, V. and Borcut, M., Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011), 4889-4897] introduced the concept of tripled fixed point and by now, there are several researches on this subject, in partially metric spaces and in cone metric spaces. In this paper, we introduce the notion of stability definition of tripled fixed point iteration procedures and establish stability results for mixed monotone mappings which satisfy various contractive conditions. Our results extend and complete some existing results in the literature. An illustrative example is also given.

Keywords

• tripled fixed point
• stability
• mixed monotone operator
• contractive condition