4 citations · 6 across the 9 of their papers we have counts for
9 papers
Metrically differentiable set-valued functions and their local linear approximants
Alona Mokhov, Nira Dyn, Elza Farkhi
A new notion of metric differentiability of set-valued functions at a point is introduced in terms of right and left limits of special set-valued metric divided differences of firs…
The pointwise limit of metric integral operators approximating set-valued functions
Elena E. Berdysheva, Nira Dyn, Elza Farkhi +1
For set-valued functions (SVFs, multifunctions), mapping a compact interval into the space of compact non-empty subsets of , we study approximation based on…
Metric approximation of set-valued functions of bounded variation by integral operators
Elena E. Berdysheva, Nira Dyn, Elza Farkhi +1
We introduce an adaptation of integral approximation operators to set-valued functions (SVFs, multifunctions), mapping a compact interval into the space of compact non-empt…
Metric Fourier approximation of set-valued functions of bounded variation
Elena E. Berdysheva, Nira Dyn, Elza Farkhi +1
We introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the parti…
From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules
Robert Baier, Elza Farkhi, Vera Roshchina
We derive exact calculus rules for the directed subdifferential defined for the class of directed subdifferentiable functions. We also state optimality conditions, a chain rule and…
Existence of Solutions for Nonconvex Differential Inclusions of Monotone Type
Elza Farkhi, Tzanko Donchev, Robert Baier
Differential inclusions with compact, upper semi-continuous, not necessarily convex right-hand sides in R^n are studied. Under a weakened monotonicity-type condition the existence…
Weak Cyclic Monotonicity and Existence of Solutions of Differential Inclusions
Elza Farkhi
The notion of weak cyclic monotonicity of set-valued maps generalizing the cyclic monotonicity is introduced. The existence of solutions of differential inclusions with compact, up…
Directed Subdifferentiable Functions and the Directed Subdifferential without Delta-Convex Structure
Robert Baier, Elza Farkhi, Vera Roshchina
We show that the directed subdifferential introduced for differences of convex (delta-convex, DC) functions by Baier and Farkhi can be constructed from the directional derivative w…
Approximations of Set-Valued Functions by Metric Linear Operators
Nira Dyn, Elza Farkhi, Alona Mokhov
In this work, we introduce new approximation operators for univariate set-valued functions with general compact images. We adapt linear approximation methods for real-valued functi…