-stability of Picard iteration in metric spaces.
The aftermath of the intermediate value theorem.
The application of fixed point theorems to global nonlinear controllability problems.
The Banach contraction mapping principle and cohomology
By a dynamical system we mean the action of the semigroup on a metrizable topological space induced by a continuous selfmap . Let denote the set of all compatible metrics on the space . Our main objective is to show that a selfmap of a compact space is a Banach contraction relative to some if and only if there exists some which, regarded as a -cocycle of the system , is a coboundary.
The Banach fixed point method for Ito stochastic differential equations
The best approximation and an extension of a fixed point theorem of F. E. Browder.
The solutions of the series-like iterative equation with variable coefficients.
The characteristic of noncompact convexity and random fixed point theorem for set-valued operators
Let be a measurable space, a Banach space whose characteristic of noncompact convexity is less than 1, a bounded closed convex subset of , the family of all compact convex subsets of We prove that a set-valued nonexpansive mapping has a fixed point. Furthermore, if is separable then we also prove that a set-valued nonexpansive operator has a random fixed point.
The common fixed point set of commuting nonexpansive mappings in Cartesian products of separable spaces
In this note we derive a theorem about the common fixed point set of commuting nonexpansive mappings defined in Cartesian products of separable spaces. The proof is based on a method due to R. E. Bruck.
The control agglomerations of an internet network with delay feedback.
The convergence of an implicit mean value iteration.
The convergence of mean value iteration for a family of maps.
The Convergence of Successive Approximations for Boundary Value Problems of Hyperbolic Equations in the Banach Space
The distance between fixed points of some pairs of maps in Banach spaces and applications to differential systems
Let be a -contraction on a Banach space and let be an almost -contraction, i.e. sum of an -contraction with a continuous, bounded function which is less than in norm. According to the contraction principle, there is a unique element in for which If moreover there exists in with , then we will give estimates for Finally, we establish some inequalities related to the Cauchy problem.
The dual form of Knaster-Kuratowski-Mazurkiewicz principle in hyperconvex metric spaces and some applications
In this paper, we first establish the dual form of Knaster- Kuratowski-Mazurkiewicz principle which is a hyperconvex version of corresponding result due to Shih. Then Ky Fan type matching theorems for finitely closed and open covers are given. As applications, we establish some intersection theorems which are hyperconvex versions of corresponding results due to Alexandroff and Pasynkoff, Fan, Klee, Horvath and Lassonde. Then Ky Fan type best approximation theorem and Schauder-Tychonoff fixed point...
The equivalence between -stabilities of the Krasnoselskij and the Mann iterations.
The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous -strongly accretive operators in uniformly smooth Banach spaces.
The equivalence between the Mann and Ishikawa iterations dealing with generalized contractions.
The equivalence between the -stabilities of Picard–Banach and Mann–Ishikawa iterations.
The equivalence of Mann iteration and Ishikawa iteration for -uniformly pseudocontractive or -uniformly accretive maps.