Introduction. The primary aim of this report is to present a broad outline for a coherent geometric theory of certain aspects of nonlinear functional analysis. Its setting requires the calculus in topological vector spaces, differential geometry of infinite dimensional manifolds, and the algebraic and differential topology of function spaces. For the most part the developments are of quite rece...

In this article, we investigate sufficient conditions for controllability of second-order semi-linear damped neutral functional initial value problem for the class of differential inclusions in Banach spaces using the theory of strongly continuous cosine families. We shall rely on a fixed point theorem due to Ma for multi-valued maps. An example is provided to illustrate the result. This work i...

We give a meaning to derivative of a function u : → X, where X is a complete metric space. This enables us to investigate differential equations in a metric space. One can prove in particular Gronwall’s Lemma, Peano and Picard Existence Theorems, Lyapunov Theorem or Nagumo Theorem in metric spaces. The main idea is to define the tangent space TxX of x ∈ X. Let u, v : [0, 1) → X, u(0) = v(0) be ...

This paper is intended as an introduction to noncommutative geometry for readers with some knowledge of abstract algebra and differential geometry. We show how to extend the theory of differential forms to the “noncommutative spaces” studied in noncommutative geometry. We formulate and prove the Hochschild-Kostant-Rosenberg theorem and an extension of this result involving the Connes differential.

The concepts of metric spaces (complete and incomplete) and associated topics are illustrated and used to prove existence and uniqueness theorems in the theory of differential equations.

Differential entropy is the entropy of a continuous random variable. It is related to the shortest description length and thus similar to the entropy of a discrete random variable. A basic introduction can be found in the book of Cover and Thomas [1]. In this paper, we are interested in the concept of shortest description length. Indeed, in a recent paper [2], we have investigated the case of s...

We study general deformation structures on path spaces defined on manifolds and specialioze to those with memory. Furthermore, we highlight the construction of local operators on path space relatively compact to some position operator. The idea of this rather elementary work is to engage in the study of how perturbative string theory could be seen as a representation of a non commutative geomet...

This paper presents a review and summary of recent research on the boundary value problems for linear ordinary and partial differential equations, with special attention to the investigations of the current authors emphasizing the applications of complex symplectic spaces. In the first part of the previous century, Stone and von Neumann formulated the theory of self-adjoint extensions of symmet...

This paper aims at establishing the existence of results for a nonstandard equilibrium problems $(EP_{N})$. The solutions of this inequality are discussed in a subset $K$ (either bounded or unbounded) of a Banach spaces $X$. Moreover, we enhance the main results by application of some differential inclusion.