The purpose of this paper is to study the convergence problem of Mann and Ishikawa type iterative schemes of weakly contractive mapping in a complete convex metric space. We establish the results on invariant approximation for the mapping defined on a class of nonconvex sets in a convex metric space. Finally, we obtain the existence of common fixed points of two asymptotically nonexpansive mapp...

Since the fundamental theory of variational inequality was founded in the 1960s, the variational inequality theory with applications has made powerful progress and has become an important part of nonlinear analysis. It has been applied intensively to mechanics, differential equation, cybernetics, quantitative economics, optimization theory, nonlinear programming, and so forth (see [2]). In virt...

Let A and B be two nonempty subsets of a metric space X. A mapping T : A∪B → A∪B is said to be noncyclic if T (A) ⊆ A and T (B) ⊆ B. For such a mapping, a pair (x, y) ∈ A×B such that Tx = x, Ty = y and d(x, y) = dist(A,B) is called a best proximity pair. In this paper we give some best proximity pair results for noncyclic mappings under certain contractive conditions.

We define sequential completeness for ⊤-quasi-uniform spaces using Cauchy pair ⊤-sequences. show that implies and ⊤-uniform with countable bases, are equivalent. As an illustration of the applicability concept, we give a fixed point theorem certain contractive self-mappings in space. This result yields, as special case, probabilistic metric spaces.

Aiming at a fast and robust simulation of large multibody systems with contacts and friction, this work presents a novel solution method which can solve large complementarity problems by means of a fixed-point iteration. When thousands of unilateral constraints are added to the system, our method performs like a Banach contractive mapping, providing a fast monotonic approximation to the exact L...