-stability of Picard iteration in metric spaces.
The Alexandroff-Urysohn square and the fixed point property.
The Banach contraction mapping principle and cohomology.
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 best approximation and an extension of a fixed point theorem of F. E. Browder.
The boundary-Wecken classification of surfaces.
The control agglomerations of an internet network with delay feedback.
The convergence of mean value iteration for a family of maps.
The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous -strongly accretive operators in uniformly smooth Banach spaces.
The fixed point index for accretive mapping with -set contraction perturbation in cones.
The Fixed Point Index of Fibre-Preserving Maps.
The fixed point property for set-valued mappings
The fixed point property for set-valued mappings of some acyclic curves
The fixed point property for some cartesian products
It is proved that the cylinder X × I over a planar λ-dendroid X has the fixed point property. This is a partial solution of two problems posed by R. H. Bing (cf. [1], Questions 9 and 10).
The fixed-point property for deformations of tree-like continua
Let f be a map of a tree-like continuum M that sends each arc-component of M into itself. We prove that f has a fixed point. Hence every tree-like continuum has the fixed-point property for deformations (maps that are homotopic to the identity). This result answers a question of Bellamy. Our proof resembles an old argument of Brouwer involving uncountably many tangent curves. The curves used by Brouwer were originally defined by Peano. In place of these curves, we use rays that were originally defined...
The Idzik type quasivariational inequalities and noncompact optimization problems
The indexed open covering theorem
The Kannan's fixed point theorem in a cone rectangular metric space.
The multicores in metric spaces and their application in fixed point theory
This paper discusses the notion, the properties and the application of multicores, i.e. some compact sets contained in metric spaces.
The Schauder fixed point theorem