Implicit Functions from Topological Vector Spaces to Banach Spaces

Finite order differentiability properties, fixed points and implicit functions over valued fields

We prove an implicit function theorem for C^k-maps from arbitrary topological vector spaces over valued fields to Banach spaces (for k at least 2). As a tool, we show the C^k-dependence of fixed points on parameters for suitable families of contractions of a Banach space. Similar results are obtained for k times strictly differentiable maps, and for k times Lipschitz differentiable maps. In the real case, our results subsume an implicit function theorem for Keller C^k_c-maps from arbitrary topological vector spaces to Banach spaces.

On the Banach-Stone Theorem and the Manifold Topological Classification

We present a simple set-theoretic proof of the Banach-Stone Theorem .We thus apply this Topological classification theorem to the still unsolved problem of topological classification of euclidean manifolds through two conjectures and additionally we give a straightforward proof of the famous Brower theorem for Manifolds topologically classified by their euclidean dimensions.

拓扑空间中的关系论Banach压缩原理及其应用

Relation-Theoretic Banach Contraction Principle in Topological Spaces with an Application

该研究将关系论概念推广至拓扑空间，引入保关系压缩映射以拓展Banach压缩原理，通过算例和MATLAB可视化验证有效性，并应用于分数阶微分方程求解。

Stochastic processes on non-Archimedean spaces. III. Stochastic processes on totally disconnected topological groups

Stochastic processes on totally disconnected topological groups are investigated. In particular they are considered for diffeomorphism groups and loop groups of manifolds on non-Archimedean Banach spaces. Theorems about a quasi-invariance and a pseudo-differentiability of transition measures are proved. Transition measures are used for the construction of strongly continuous representations including irreducible of these groups. In addition stochastic processes on general Banach-Lie groups, loop monoids, loop spaces and path spaces of manifolds on Banach spaces over non-Archimedean local field…

Some existence and stability results of Hilfer-Hadamard fractional implicit differential fractional equation in a weighted space

This paper studies a nonlinear fractional implicit differential equation (FIDE) with boundary conditions involving a HilferHadamard type fractional derivative. We establish the equivalence between the Cauchy-type problem (FIDE) and its mixed type integral equation through a variety of tools of some properties of fractional calculus and weighted spaces of continuous functions. The existence and uniqueness of solutions are obtained. Further, the Ulam-Hyers and Ulam-Hyers-Rassias stability are discussed. The arguments in the analysis rely on Schaefer fixed point theorem, Banach contraction princi…