Abstract
We first introduce the concept of a triangular 2-alpha-eta-admissible mapping which extends the notion of alpha-admissible mapping with respect to eta to 2-metric spaces. Next, we introduce the concepts of modified weak and modified rational alpha-psi-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.