Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1203.54051
Włodarczyk, Kazimierz; Plebaniak, Robert; Doliński, Mariusz
Cone uniform, cone locally convex and cone metric spaces, endpoints, set-valued dynamic systems and quasi-asymptotic contractions. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 10, A, 5022-5031 (2009). ISSN 0362-546X

Summary: The concepts of cone pseudometrics, cone uniform spaces generated by these pseudometrics, cone pseudodistances, set-valued quasi-asymptotic contractions with respect to these pseudodistances, and cone closed maps are introduced and studied. Conditions guaranteeing the existence and uniqueness of endpoints (stationary points) of these contractions and conditions ensuring that, for each starting point, each generalized sequence of iterations of these contractions (in particular, each dynamic process) converges, and then the limit is an endpoint, are all established. Also, the concept of the cone locally convex space as a special case of the cone uniform space is introduced and examples of quasi-asymptotic contractions in cone metric spaces are constructed. The definitions, results, ideas and methods are new for set-valued dynamic systems in cone uniform, cone locally convex and cone metric spaces and even for single-valued maps in these spaces.

MSC 2000:: *54H25 Fixed-point theorems in topological spaces
54E15 Uniform structures and generalizations
54C60 Set-valued maps

Keywords: cone uniform space; cone pseudometric; cone pseudodistance; quasi-asymptotic contraction; uniqueness of endpoint; set-valued dynamic system; cone locally convex space; cone metric space; cone closed map; generalised sequence of iterations; dynamic process

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]