(untitled) (Communications in Mathematical Research, 2019)
In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function φ to construct a new implicit-linear contractive condition and obtain some existence theorems of common fixed points for two mappings on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point. The obtained results well generalize and improve the corresponding conclusions in references.