Multivariate contraction mapping principle with the error estimate formulas in locally convex topological vector spaces and application

Abstract

The purpose of this paper is to present the concept of multivariate contraction mapping in a locally convex topological vector spaces and to prove the multivariate contraction mapping principle in such spaces. The neighborhood-type error estimate formulas are also established. The results of this paper improve and extend Banach contraction mapping principle in the new idea.

Multivariate systems of nonexpansive operator equations and iterative algorithms for solving them in uniformly convex and uniformly smooth Banach spaces with applications

“…In 2016, Luo, Su, and Gao [ 6 ] presented the concept of a multivariate best proximity point and proved multivariate best proximity point theorems in metric spaces for N -variable contraction mappings. In 2017, Xu et al [ 8 ] presented the concept of a multivariate contraction mapping in a locally convex topological vector space and proved the multivariate contraction mapping principle in such spaces. In 2017, Guan et al [ 4 ] studied a certain system of N -fixed point operator equations with N -pseudo-contractive mapping in reflexive Banach spaces and proved existence theorems of solutions.…”

A kind of system of multivariate variational inequalities and the existence theorem of solutions

“…In 2016, Luo et al [ 18 ] presented the concept of multivariate best proximity point and proved the multivariate best proximity point theorems in metric spaces for N -variables contraction mappings. In 2017, Xu et al [ 19 ] presented the concept of multivariate contraction mapping in a locally convex topological vector spaces and proved the multivariate contraction mapping principle in such spaces. In 2017, Guan et al [ 20 ] studied a kind of system of N -variables pseudocontractive operator equations and proved the existence theorem of solutions.…”