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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |