Dynamic Processes, Fixed Points, Endpoints, Asymmetric Structures, and Investigations Related to Caristi, Nadler, and Banach in Uniform Spaces

Abstract EN

In uniform spaces X, D with symmetric structures determined by theD-families of pseudometrics which define uniformity in these spaces, thenew symmetric and asymmetric structures determined by the J-familiesof generalized pseudodistances on X are constructed; using these structures the set-valued contractions of two kinds of Nadler type are definedand the new and general theorems concerning the existence of fixed pointsand endpoints for such contractions are proved.

Moreover, using these newstructures, the single-valued contractions of two kinds of Banach type aredefined and the new and general versions of the Banach uniqueness anditerate 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 ofour fixed point and endpoint version of Caristi type theorem for dissipative set-valued dynamic systems without lower semicontinuous entropiesin uniform spaces with structures determined by J-families.

Results arenew also in locally convex and metric spaces.

Examples are provided.