Typically, big bang bifurcation occurs for one (or higher)-dimensional piecewise-defined systems whenever two border collision bifurcation curves collide transversely in the parameter space. At that point, two (feasible) fixed points collide with the boundary in state space and become virtual. Depending on the properties of the map at the colliding fixed points, there exist different scenarios ...

Let X, d be a complete metric space and T a self-map of X. Let xn 1 f T, xn be some iteration procedure. Suppose that F T , the fixed point set of T , is nonempty and that xn converges to a point q ∈ F T . Let {yn} ⊂ X and define n d yn 1, f T, yn . If lim n 0 implies that limyn q, then the iteration procedure xn 1 f T, xn is said to be T -stable. Without loss of generality, we may assume that ...

Let E be a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm. Let J {T t : t ≥ 0} be a family of uniformly asymptotically regular generalized asymptotically nonexpansive semigroup of E, with functions u, v : 0,∞ → 0,∞ . Let F : F J ∩t≥0F T t / ∅ and f : K → K be a weakly contractive map. For some positive real numbers λ and δ satisfying δ λ > 1, let G ...

Recently, there has been an outburst of interest in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. The representational capabilities and internal representations of the models are not well understood. We concentrate on a generalization of the Self-Organizing Map (SOM) for processing sequential data – the Recursive SOM (RecSOM [1]). We a...

The purpose of this paper is to present the definition of [Formula: see text]-contractive mapping and to discuss the relation of [Formula: see text]-contractive mappings and [Formula: see text]-contractive mappings. Furthermore, the generalized [Formula: see text]-contraction mapping principle has been proved without the uniqueness condition. Meanwhile, the generalized [Formula: see text]-contr...

Abstract In the present paper concepts of q-rung orthopair fuzzy mappings (q-ROF mapping) and $( \alpha ,\beta ) $ ( α , β ) -cuts are introduced. Some common fixed point results for q-ROF presented in b-metric spaces using Suzuki-type contra...

In order to solve domain equations over 1-bounded compact metric spaces, xed points of functors on categories of 1-bounded compact metric spaces are studied. Two categories of 1-bounded compact metric spaces are considered: KMS and KMS E. In both categories, objects are isomorphic if and only if they are isometric. As a consequence, provided that the operation of a domain equation can be extend...

we provide fuzzy quasi-metric versions of a fixed point theorem ofgregori and sapena for fuzzy contractive mappings in g-complete fuzzy metricspaces and apply the results to obtain fixed points for contractive mappingsin the domain of words.