Related papers: On Directional Derivatives for cone-convex funtion…
In the present paper we investigate the existence of directional derivatives for strongly cone-paraconvex mappings. Our result is a counterpart of the theorem of Valadier concerning directional differentiability of cone convex mappings.
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 .
In the paper we discuss conformable derivative behavior in arbitrary Banach spaces and clear the connection between two conformable derivatives of different order. As a consequence we obtain the important result that an abstract function…
A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…
Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent…
This paper addresses the study and characterizations of variational convexity of extended-real-valued functions on Banach spaces. This notion has been recently introduced by Rockafellar, and its importance has been already realized and…
We show that the existence of a strongly convex function with a Lipschitz derivative on a Banach space already implies that the space is isomorphic to a Hilbert space. Similarly, if both a function and its convex conjugate are $C^2$ then…
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.
In this paper directional derivative sets and differentials of a given set valued map are studied. Relations between the set valued map and compact subsets of the directional derivative sets of the given map are investigated. Upper and…
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.…
We show that the derivatives in the sense of Fr\'echet and G\^ateaux can be viewed as derivatives oriented towards a star convex set with the origin as center. The resulting oriented differential calculus extends the mean value theorem, the…
We prove implicit function theorems for mappings on topological vector spaces over valued fields. In the real and complex cases, we obtain implicit function theorems for mappings from arbitrary (not necessarily locally convex) topological…
We compute the derived functors of (the functors associated to) the ideal of compact operators in Banach spaces and obtain new results about the extension and lifting of compact operators.
In this paper we study the Y-convexity, a property which is obtained by considering a real Banach sequence lattice Y instead of $\ell^p$ for a linear operator $T : E \rightarrow X$, where E is a Banach space and X is a Banach lattice. We…
We provide sufficient conditions for the existence of a strong derivable map and calculate its derivative by employing a result in our previous work on strong derivability of maps arising by functional calculus of an unbounded scalar type…
Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X. Let Pc from X to C denote the (standard) metric projection operator. In this paper, we define the Gateaux directional…
In this paper, we investigate the properties of the Mordukhovich derivatives of the metric projection operator onto closed balls, closed and convex cylinders and positive cones in uniformly convex and uniformly smooth Banach spaces. We find…
We develop differential calculus of $C^{r,s}$-mappings on products of locally convex spaces and prove exponential laws for such mappings. As an application, we consider differential equations in Banach spaces depending on a parameter in a…
This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus,…
Our basic element is a $C^1$ mapping $f:X\to Y$, with $X,Y$ Banach spaces, and with derivative everywhere invertible. So $f$ is a local diffeomorphism at every point. The aim of this paper is to find a sufficient condition for $f$ to be…