Dynamic Processes, Fixed Points, Endpoints, Asymmetric Structures, and Investigations Related to Caristi, Nadler, and Banach in Uniform Spaces
In uniform spaces X, D with symmetric structures determined by the D-families of pseudometrics which define uniformity in these spaces, the new symmetric and asymmetric structures determined by the J-families of generalized pseudodistances on X are constructed; using these structures the set-valued...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/942814 |
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| author | Kazimierz Włodarczyk Robert Plebaniak |
| author_facet | Kazimierz Włodarczyk Robert Plebaniak |
| author_sort | Kazimierz Włodarczyk |
| collection | DOAJ |
| description | In uniform spaces X, D with symmetric structures determined by the
D-families of pseudometrics which define uniformity in these spaces, the
new symmetric and asymmetric structures determined by the J-families
of generalized pseudodistances on X are constructed; using these structures the set-valued contractions of two kinds of Nadler type are defined
and the new and general theorems concerning the existence of fixed points
and endpoints for such contractions are proved. Moreover, using these new
structures, the single-valued contractions of two kinds of Banach type are
defined and the new and general versions of the Banach uniqueness and
iterate approximation of fixed point theorem for uniform spaces are established. Contractions defined and studied here are not necessarily continuous. One of the main key ideas in this paper is the application of
our fixed point and endpoint version of Caristi type theorem for dissipative set-valued dynamic systems without lower semicontinuous entropies
in uniform spaces with structures determined by J-families. Results are
new also in locally convex and metric spaces. Examples are provided. |
| format | Article |
| id | doaj-art-4ba3d0de13024ba0913fee97dbcba422 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-4ba3d0de13024ba0913fee97dbcba4222025-02-03T01:04:51ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/942814942814Dynamic Processes, Fixed Points, Endpoints, Asymmetric Structures, and Investigations Related to Caristi, Nadler, and Banach in Uniform SpacesKazimierz Włodarczyk0Robert Plebaniak1Department of Nonlinear Analysis, Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, PolandDepartment of Nonlinear Analysis, Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, PolandIn uniform spaces X, D with symmetric structures determined by the D-families of pseudometrics which define uniformity in these spaces, the new symmetric and asymmetric structures determined by the J-families of generalized pseudodistances on X are constructed; using these structures the set-valued contractions of two kinds of Nadler type are defined and the new and general theorems concerning the existence of fixed points and endpoints for such contractions are proved. Moreover, using these new structures, the single-valued contractions of two kinds of Banach type are defined and the new and general versions of the Banach uniqueness and iterate approximation of fixed point theorem for uniform spaces are established. Contractions defined and studied here are not necessarily continuous. One of the main key ideas in this paper is the application of our fixed point and endpoint version of Caristi type theorem for dissipative set-valued dynamic systems without lower semicontinuous entropies in uniform spaces with structures determined by J-families. Results are new also in locally convex and metric spaces. Examples are provided.http://dx.doi.org/10.1155/2015/942814 |
| spellingShingle | Kazimierz Włodarczyk Robert Plebaniak Dynamic Processes, Fixed Points, Endpoints, Asymmetric Structures, and Investigations Related to Caristi, Nadler, and Banach in Uniform Spaces Abstract and Applied Analysis |
| title | Dynamic Processes, Fixed Points, Endpoints, Asymmetric Structures, and Investigations Related to Caristi, Nadler, and Banach in Uniform Spaces |
| title_full | Dynamic Processes, Fixed Points, Endpoints, Asymmetric Structures, and Investigations Related to Caristi, Nadler, and Banach in Uniform Spaces |
| title_fullStr | Dynamic Processes, Fixed Points, Endpoints, Asymmetric Structures, and Investigations Related to Caristi, Nadler, and Banach in Uniform Spaces |
| title_full_unstemmed | Dynamic Processes, Fixed Points, Endpoints, Asymmetric Structures, and Investigations Related to Caristi, Nadler, and Banach in Uniform Spaces |
| title_short | Dynamic Processes, Fixed Points, Endpoints, Asymmetric Structures, and Investigations Related to Caristi, Nadler, and Banach in Uniform Spaces |
| title_sort | dynamic processes fixed points endpoints asymmetric structures and investigations related to caristi nadler and banach in uniform spaces |
| url | http://dx.doi.org/10.1155/2015/942814 |
| work_keys_str_mv | AT kazimierzwłodarczyk dynamicprocessesfixedpointsendpointsasymmetricstructuresandinvestigationsrelatedtocaristinadlerandbanachinuniformspaces AT robertplebaniak dynamicprocessesfixedpointsendpointsasymmetricstructuresandinvestigationsrelatedtocaristinadlerandbanachinuniformspaces |