𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The uniqueness of endpoints for set-valued dynamical systems of contractions of Meir–Keeler type in uniform spaces

✍ Scribed by Kazimierz Włodarczyk; Robert Plebaniak; Cezary Obczyński

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
263 KB
Volume
67
Category
Article
ISSN
0362-546X

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, the concept of the set-valued dynamical systems of contractions of Meir-Keeler type in uniform spaces is introduced and conditions guaranteeing the existence and uniqueness of endpoints of these contractions and the convergence to these endpoints of all generalized sequences of iterations of these contractions are established. The definition and the result presented here are new for set-valued dynamical systems in uniform, locally convex and metric spaces and even for single-valued maps. Examples show a fundamental difference between our result and the well-known ones.

📜 SIMILAR VOLUMES

Endpoints of set-valued dynamical system
Endpoints of set-valued dynamical systems of asymptotic contractions of Meir–Keeler type and strict contractions in uniform spaces
✍ Kazimierz Włodarczyk; Robert Plebaniak; Cezary Obczyński 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 289 KB

In this paper, we introduce the concepts of the set-valued dynamical systems of asymptotic contractions of Meir-Keeler type and set-valued dynamical systems of strict contractions in uniform spaces and we present a method which is useful for establishing conditions guaranteeing the existence and uni

Convergence theorems, best approximation
Convergence theorems, best approximation and best proximity for set-valued dynamic systems of relatively quasi-asymptotic contractions in cone uniform spaces
✍ Kazimierz Włodarczyk; Robert Plebaniak; Cezary Obczyński 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 1004 KB

In cone uniform spaces X , using the concept of the D-family of cone pseudodistances, the distance between two not necessarily convex or compact sets A and B in X is defined, the concepts of cyclic and noncyclic set-valued dynamic systems of D-relatively quasiasymptotic contractions T : A ∪ B → 2 A∪