A mapping theorem on g-metrizable spaces

The Existence Theorem for Contractive Mappings on $wt$-distance in $b$-metric Spaces Endowed with a Graph and its Application

In this paper, we study the existence and uniqueness of fixed points for mappings with respect to a $wt$-distance in $b$-metric spaces endowed with a graph. Our results are significant, since we replace the condition of continuity of mapping with the condition of orbitally $G$-continuity of mapping and we consider $b$-metric spaces with graph instead of $b$-metric spaces, under which can be gen...

ON LOCAL HUDETZ g-ENTROPY

In this paper, a local approach to the concept of Hudetz $g$-entropy is presented. The introduced concept is stated in terms of Hudetz $g$-entropy. This representation is based on the concept of $g$-ergodic decomposition which is a result of the Choquet's representation Theorem for compact convex metrizable subsets of locally convex spaces.

A factorization theorem for the transfinite kernel dimension of metrizable spaces

We prove a factorization theorem for transfinite kernel dimension in the class of metrizable spaces. Our result in conjunction with Pasynkov’s technique implies the existence of a universal element in the class of metrizable spaces of given weight and transfinite kernel dimension, a result known from the work of Luxemburg and Olszewski.

Sn-metrizable Spaces and Related Matters

sn-networks were first introduced by Lin [12], which are the concept between weak bases and cs-networks. sn-metrizable spaces [6] (i.e., spaces with σ-locally finite sn-networks) are one class of generalized metric spaces, and they play an important role in metrization theory, see [6, 13]. In this paper, we give a mapping theorem on sn-metrizable spaces, discuss relationships among spaces with ...

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition