In this paper, we continue the study of contractive conditions for mappings in complete partial metric spaces. Concretely, we present fixed point results for weakly contractive and weakly Kannan mappings in such a way that the classical metric counterpart results are retrieved as a particular case. Special attention to the cyclical case is paid. Moreover, the well-posedness of the fixed point p...

Transversality phenomena are studied for homology manifolds. For homology manifolds X, Y and Z, with Z embedded in Y with a neighborhood ν(Z) which has a given bundle structure, we define a map f : X → Y to be transverse to Z, if f−1(Z) = Z′ is a homology manifold, the neighborhood f−1(ν(Z)) has a bundle structure given by f∗ν(Z) and f induces the bundle map. In the case where the range is a ma...

We find concrete necessary and sufficient conditions for the existence of contractive completions of Hankel partial contractions of size 4×4 in the extremal case. Along the way we introduce a new approach that allows us to solve, algorithmically, the contractive completion problem for 4 × 4 Hankel matrices. As an application, we obtain a concrete example of a partially contractive 4× 4 Hankel m...

Barnsley (2006) introduced the notion of a fractal top, which is an addressing function for the set attractor of an Iterated Function System (IFS). A fractal top is analogous to a set attractor as it is the fixed point of a contractive transformation. However, the definition of IFS is extended so that it works on the colour component as well as the spatial part of a picture. They can be used to...

We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the “separation property”: different continuity pieces have disjoint images. The continuity pieces act as stable topological manifolds while the points in the discontinuity lines, separating different conti...

Let E be a real reflexive Banach space with a uniformly Gâteaux differentiable norm. Let K be a nonempty bounded closed convex subset of E, and every nonempty closed convex bounded subset of K has the fixed point property for non-expansive self-mappings. Let f : K → K a contractive mapping and T : K → K be a uniformly continuous pseudocontractive mapping with F T / ∅. Let {λn} ⊂ 0, 1/2 be a seq...

An affine iterated function system (IFS, [4]) over the reals is given by a set of contractive affine transformations on a complete metric space R for some positive natural number k. Thus an interesting problem is to decide, whether a given matrix M describes a contraction mapping, i.e. whether there exists some s < 1 such that |Mz| ≤ s|z| for each z ∈ R, where | · | denotes the Euclidean norm. ...

*Correspondence: [email protected] 2Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, 10140, Thailand Full list of author information is available at the end of the article Abstract We set up a new variant of cyclic generalized contractive mappings for a map in a metric space and present existence and uniqueness results of fixed...

*Correspondence: [email protected] 1School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China Full list of author information is available at the end of the article Abstract Based on the concept and properties of C∗-algebras, the paper introduces a concept of C∗-algebra-valued b-metric spaces which generalizes the concept of C∗-algebra-valued metric spac...

We are concerned with function approximation and image representation using Iterated Function Systems (IFS) over L p (X;): An N-map IFS with grey level maps (IFSM), to be denoted as (w;), is a set w of N contraction maps w i : X ! X over a compact metric space (X; d) (the \base space") with an associated set of maps i : R ! R. Associated with each IFSM is a contractive operator T with xed point...