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 …

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 …

In this paper we give an overview of mapping, continuity and boundedness properties of
nonlinear composition operators of type Hf (t):= h (f (t)) or Hf (t):= h (t, f (t)) in the function …

Functions of bounded variation are most important in many fields of mathe¬ matics. This
thesis investigates spaces of functions of bounded variation with one variable of various …

Czechoslovak Mathematical Journal Page 1 Czechoslovak Mathematical Journal Nelson
Merentes; Sergio Rivas On characterization of the Lipschitzian composition operator between …

Let R [a, b] be the algebra of all real functions f:[a, b]→ R on the closed interval [a, b], BV [a,
b] be the subalgebra of functions of bounded (in the sense of Jordan) variation in R [a, b] …

We give a necessary and sufficient condition on a function f: R → R under which the
composition operator (Nemytskij operator) F defined by Fh= f ∘ h acts in the spaces BV_ φ a …

We present necessary and sufficient conditions on the generating functions of operators of
substitution (= Nemytskii superposition operators), which map the Waterman space v BV of …

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 …

We prove that if the composition operator F generated by a function f:[a, b]× ℝ→ ℝ maps the
space of bounded (p, k)-variation in the sense of Riesz-Popoviciu, p≥ 1, k an integer …