Metrizability of Topological Vector Space Valued Cone Metric Spaces

单值与多值希尔伯特丛的重赋范

Single and multi-valued Hilbert-bundle renormings

该研究证明紧可度量化空间上的次齐次连续巴拿赫丛等价于希尔伯特丛，说明可度量化假设不可完全去掉，补充了齐次丛的对应结论并推广了次齐次$C^*$丛的相关结果。

Completeness Properties of the open-point and bi-point-open topologies on C(X)

This paper studies various completeness properties of the open-point and bi-point-open topologies on the space C(X) of all real-valued continuous functions on a Tychonoff space X. The properties range from complete metrizability to the Baire space property.

Fixed Point Theorems for Set-Valued Mappings on TVS-Cone Metric Spaces

In the context of tvs-cone metric spaces, we prove a Bishop-Phelps and a Caristi's type theorem. These results allow us to prove a fixed point theorem for $(δ, L)$-weak contraction according to a pseudo Hausdorff metric defined by means of a cone metric.

Topological Properties of the Space of Convex Minimal Usco Maps

Let X be a Tychonoff space and MC(X) be the space of convex minimal usco maps with values in R, the space of real numbers. Such set-valued maps are important in the study of subdifferentials of convex functions. Using the strong Choquet game we prove complete metrizability of MC(X) with the upper Vietoris topology. If X is normal, elements of MC(X) can be approximated in the Vietoris topology by continuous functions. We also study first countability, second countability and other properties of the upper Vietoris topology on MC(X).

Locally Convex Valued Rectangular Metric Spaces and The Kannan's Fixed Point Theorem

Rectangular TVS-cone metric spaces are introduced and Kannan's fixed point theorem is proved in these spaces. Two approaches are followed for the proof. At first we prove the theorem by a direct method using the structure of the space itself. Secondly, we use the nonlinear scalarization used recently by Wei-Shih Du in [A note on cone metric fixed point theory and its equivalence, {Nonlinear Analysis},72(5),2259-2261 (2010).] to prove the equivalence of the Banach contraction principle in cone metric spaces and usual metric spaces. The proof is done without any normality assumption on the cone …

统计p向上拟柯西序列与锥值连续性

Statistically p-Upward Quasi-Cauchy Sequences and Cone-Valued Continuity

本文研究了统计p向上拟柯西序列及其连续性，定义了新的函数空间并探讨了其性质与应用。