Applying the theory of modular metric spaces developed in the first part of this paper [VV
Chistyakov (2009)[1]] we define a metric semigroup and an abstract convex cone of …

The paper presents recent results concerning the problem of the existence of those
selections, which preserve the properties of a given set-valued mapping of one real variable …

Abstract top CONTENTSIntroduction.....................................................................................................
..... 51. Multifunctions and selections............................................................................... 7 1 …

We study (set-valued) mappings of bounded Φ-variation defined on the compact interval I
and taking values in metric or normed linear spaces X. We prove a new structural theorem …

We sonsider the Nemytskii operator, ie the composition operator defined by (Nu)(t)= H (t, u
(t)), where H is a given set-valued function. It is shown that if the operator N maps the space …

We define and study the metric semigroup BV 2 (I ab; M) of mappings of two real variables of
bounded total variation in the Vitali-Hardy-Krause sense on a rectangle I ab with values in a …

In this paper, we show that if the Nemytskii operator maps the (p, α)-bounded variation
space into itself and satisfies some Lipschitz condition, then there are two functions g and h …

Let (X,∥·∥) and (Y,∥·∥) be two normed spaces and K be a convex cone in X. Let CC (Y)
be the family of all non-empty convex compact subsets of Y. We consider the Nemytskiĭ …

En este artículo demostramos que si el operador de Nemytskii lleva el espacio de variación
(φ, α)-acotada en sí mismo, y satisface cierta condición de Lipschitz, entonces existen dos …

Functions of bounded variation are fascinating mathematical objects which, since their
definition by C. Jordan more than a century ago, have found much attention in real analysis …