Related papers: About Conformable Derivatives in Banach Spaces

We investigate the relationship between the existence of directional derivatives for cone-convex functions with values in a Banach space Y and isomorphisms between Y and c0.

This paper discusses some unusual consequences raised by the definition of the conformable derivative in the lower terminal. A replacement for this definition is proposed and statements adjusted to the new definition are presented.

The aim of the present paper is to make some notes to the newly introduced conformable derivative as a type local fractional derivative and to present a surprising result about the relation between the conformable derivatives and the usual…

It is a longstanding problem whether every contractible Banach algebra is necessarily finite-dimensional. In this note, we confirm this for Banach algebras acting on Banach spaces with the uniform approximation property. This generalizes a…

We study the existence of global implicit functions for equations defined on open subsets of Banach spaces. The partial derivative with respect to the second variable is only required to have a left inverse instead of being invertible.…

This note aims to highlight the link between representable functionals and derivations on a Banach quasi *-algebra, i.e. a mathematical structure that can be seen as the completion of a normed *-algebra in the case the multiplication is…

In this paper, we study several type of point derivations for Banach algebras. We investigate how our definition of point derivations are related to each others.

The notion of adequate function has been recently introduced in order to characterize the essentially strictly functions on a reflexive Banach space among the weakly lower semicontinuous ones. In this paper we reinforce this concept and…

It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm which is itself locally uniformly convex. It follows that on any such space all continuous real-valued functions may be uniformly approximated by…

We provide sufficient conditions for a Banach space Y to be weakly sequentially complete. These conditions are expressed in terms of the existence of directional derivatives for cone convex mappings with values in Y .

Classes of Banach spaces that are finitely, strongly finitely or elementary equivalent are introduced. On sets of these classes topologies are defined in such a way that sets of defined classes become compact totally disconnected…

This paper is devoted to studying the first-order variational analysis of non-convex and non-differentiable functions that may not be subdifferentially regular. To achieve this goal, we entirely rely on two concepts of directional…

The question of defining unique, generally applicable constrained second, and higher-order, derivatives is investigated. It is shown that second-order constrained derivatives obtained via two successive constrained differentiations provide…

Let $X$ be a compact subset of the complex plane and $x \in X$. A necessary and sufficient condition is given in terms of Hausdorff contents for the existence of a bounded point derivation at $x$ on the space of vanishing Campanato…

Let X be a separable Banach space which admits a separating polynomial; in particular X a separable Hilbert space. Let $f:X \rightarrow R$ be bounded, Lipschitz, and $C^1$ with uniformly continuous derivative. Then for each {\epsilon}>0,…

We investigate differences between upper and lower porosity. In finite dimensional Banach spaces every upper porous set is directionally upper porous. We show the situation is very different for lower porous sets; there exists a lower…

Let $X$ be a compact Hausdorff space and $A$ a Banach algebra. We investigate amenability properties of the algebra $C(X,A)$ of all $A$-valued continuous functions. We show that $C(X,A)$ has a bounded approximate diagonal if and only if $A$…

Transports preserving the angle between two contravariant vector fields but changing their lengths proportional to their own lengths are introduced as ''conformal'' transports and investigated over spaces with contravariant and covariant…

A Banach space $X$ is called subprojective if any of its infinite dimensional subspaces $Y$ contains a further infinite dimensional subspace complemented in $X$. This paper is devoted to systematic study of subprojectivity. We examine the…

In this article we consider area preserving diffeomorphisms of planar domains, and we are interested in their conformal points, i.e., points at which the derivative is a similarity. We present some conditions that guarantee existence of…