Mann iterates of directionally nonexpansive mappings in hyperbolic spaces.
Mann iteration converges faster than Ishikawa iteration for the class of Zamfirescu operators.
Mapping theorems for compacta with an arbitrary involution
Maximality principle and general results of Ekeland and Caristi types without lower semicontinuity assumptions in cone uniform spaces with generalized pseudodistances.
Meir-Keeler contractions of integral type are still Meir-Keeler contractions.
Merging of degree and index theory.
Metric spaces admitting only trivial weak contractions
If (X,d) is a metric space then a map f: X → X is defined to be a weak contraction if d(f(x),f(y)) < d(x,y) for all x,y ∈ X, x ≠ y. We determine the simplest non-closed sets X ⊆ ℝⁿ in the sense of descriptive set-theoretic complexity such that every weak contraction f: X → X is constant. In order to do so, we prove that there exists a non-closed set F ⊆ ℝ such that every weak contraction f: F → F is constant. Similarly, there exists a non-closed set G ⊆ ℝ such that every weak contraction...
Minimal component numbers of fixed point sets
Let f: (X,A) → (X,A) be a relative map of a pair of compact polyhedra. We introduce a new relative homotopy invariant , which is a lower bound for the component numbers of fixed point sets of the self-maps in the relative homotopy class of f. Some properties of are given, which are very similar to those of the relative Nielsen number N(f;X,A).
Minimal fixed point sets of relative maps
Let f: (X,A) → (X,A) be a self map of a pair of compact polyhedra. It is known that f has at least N(f;X,A) fixed points on X. We give a sufficient and necessary condition for a finite set P (|P| = N(f;X,A)) to be the fixed point set of a map in the relative homotopy class of the given map f. As an application, a new lower bound for the number of fixed points of f on Cl(X-A) is given.
Minimal Nielsen root classes and roots of liftings.
Minimal nonhomogeneous continua
We show that there are (1) nonhomogeneous metric continua that admit minimal noninvertible maps but have the fixed point property for homeomorphisms, and (2) nonhomogeneous metric continua that admit both minimal noninvertible maps and minimal homeomorphisms. The former continua are constructed as quotient spaces of the torus or as subsets of the torus, the latter are constructed as subsets of the torus.
Monotone generalized nonlinear contractions in partially ordered metric spaces.
Monotonic mappings on ordered sets, a class of inequalities with finite differences and fixed points.
Monotonous stability for neutral fixed points.
More on tie-points and homeomorphism in ℕ*
A point x is a (bow) tie-point of a space X if X∖x can be partitioned into (relatively) clopen sets each with x in its closure. We denote this as where A, B are the closed sets which have a unique common accumulation point x. Tie-points have appeared in the construction of non-trivial autohomeomorphisms of βℕ = ℕ* (by Veličković and Shelah Steprans) and in the recent study (by Levy and Dow Techanie) of precisely 2-to-1 maps on ℕ*. In these cases the tie-points have been the unique fixed point...
Multi-valued contraction mappings in complete metric spaces
Multi-valued contraction mappings in metric spaces.
Multi-valued contraction mappings in metric spaces. (Short Communication).
Multivalued contraction with parameter
Multivalued fractals in b-metric spaces
Fractals and multivalued fractals play an important role in biology, quantum mechanics, computer graphics, dynamical systems, astronomy and astrophysics, geophysics, etc. Especially, there are important consequences of the iterated function (or multifunction) systems theory in several topics of applied sciences. It is known that examples of fractals and multivalued fractals are coming from fixed point theory for single-valued and multivalued operators, via the so-called fractal and multi-fractal...