Multivariate fixed point theorems for contractions and nonexpansive mappings with applications

Yongfu Su, Adrian Petruşel, Jen-Chih Yao
2016 Fixed Point Theory and Applications  
The first purpose of this paper is to prove an existence and uniqueness result for the multivariate fixed point of a contraction type mapping in complete metric spaces. The proof is based on the new idea of introducing a convenient metric space and an appropriate mapping. This method leads to the changing of the non-self-mapping setting to the self-mapping one. Then the main result of the paper will be applied to an initial-value problem related to a class of differential equations of first
more » ... ations of first order. The second aim of this paper is to prove strong and weak convergence theorems for the multivariate fixed point of a N-variables nonexpansive mapping. The results of this paper improve several important works published recently in the literature.
doi:10.1186/s13663-015-0493-0 fatcat:mojb5r56ujhdxl2hidqixqwhr4