Fixed point results for modified weak and rational α-Ψ- contractions in ordered 2-metric spaces

Abstract

We first introduce the concept of a triangular 2-α-ν-admissible mapping which extends the notion of α-admissible mapping with respect to ν to 2-metric spaces. Next, we introduce the concepts of modified weak and modified rational α-Ψ-contractions and establish the existence and uniqueness of fixed points for such mappings in complete 2-metric spaces. As an application of the obtained results, we prove some fixed point results in partially ordered 2-metric spaces. The presented theorems generalize and improve certain existing results in the literature and provide main results in Dung and Hang (Fixed Point Theory Appl. 2013:161, 2013) as corollaries. Moreover, some examples and an application to integral equations are provided to illustrate the usability of the obtained results. © 2014 Fathollahi et al.; licensee Springer.