On functions of bounded (p,2)-variation.
On the composition operator in RV [a,b].
On the Composition Operator in AC[a,b].
Denote by F the composition operator generated by a given function f: R --> R, acting on the space of absolutely continuous functions. In this paper we prove that the composition operator F maps the space AC[a,b] into itself if and only if f satisfies a local Lipschitz condition on R.
On characterization of the Lipschitzian composition operator between spaces of functions of bounded -variation
Characterization of globally Lipschitzian composition operators in the Banach space
We give a characterization of the globally Lipschitzian composition operators acting in the space
Remarks on strongly Wright-convex functions
Some properties of strongly Wright-convex functions are presented. In particular it is shown that a function f:D → ℝ, where D is an open convex subset of an inner product space X, is strongly Wright-convex with modulus c if and only if it can be represented in the form f(x) = g(x)+a(x)+c||x||², x ∈ D, where g:D → ℝ is a convex function and a:X → ℝ is an additive function. A characterization of inner product spaces by strongly Wright-convex functions is also given.
Functions of bounded variations on compact subsets of
In this paper we introduce the concept of bounded variation for functions defined on compact subsets of the complex plane , based on the notion of variation along a curve as defined by Ashton and Doust; We describe in detail the space so generated and show that it can be equipped, in a natural way, with the structure of a Banach algebra. We also present a necessary condition for a composition operator to act between two such spaces.
Superposition Operators in the Space of Functions of Waterman-Shiba Bounded Variation
In this paper we present a necessary condition for an autonomous superposition operator to act in the space of functions of Waterman-Shiba bounded variation. We also show that if a (general) superposition operator applies such space into itself and it is uniformly bounded, then its generating function satisfies a weak Matkowski condition.
On Bi-dimensional Second Variation
In this paper we present the concept of bounded second variation of a real valued function defined on a rectangle in . We use Hardy-Vitali type technics in the plane in order to extend the classical notion of function of bounded second variation on intervals of . We introduce the class , of all functions of bounded second variation on a rectangle , and show that this class can be equipped with a norm with respect to which it is a Banach space. Finally, we present two results that show that integrals...
A Generalization of m-Convexity and a Sandwich Theorem
Functional inequalities generalizing m-convexity are considered. A result of a sandwich type is proved. Some applications are indicated.
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In this paper we study existence and uniqueness of solutions for the Hammerstein equation in the space of function of bounded total -variation in the sense of Hardy-Vitali-Tonelli, where , and are suitable functions. The existence and uniqueness of solutions are proved by means of the Leray-Schauder nonlinear alternative and the Banach contraction mapping principle.
On Korenblum convex functions
We introduce a new class of generalized convex functions called the -convex functions, based on Korenblum’s concept of -decreasing functions, where is an entropy (distortion) function. We study continuity and differentiability properties of these functions, and we discuss a special subclass which is a counterpart of the class of so-called d.c. functions. We characterize this subclass in terms of the space of functions of bounded second -variation, extending a result of F. Riesz. We also present...
Some remarks on the algebra of functions of two variables with bounded total -variation in Schramm sense
This paper is devoted to discuss some generalizations of the bounded total -variation in the sense of Schramm. This concept was defined by W. Schramm for functions of one real variable. In the paper we generalize the concept in question for the case of functions of of two variables defined on certain rectangle in the plane. The main result obtained in the paper asserts that the set of all functions having bounded total -variation in Schramm sense has the structure of a Banach algebra.
A Representation Theorem for -Bounded Variation of Functions in the Sense of Riesz
In this paper we extend the well known Riesz lemma to the class of bounded -variation functions in the sense of Riesz defined on a rectangle . This concept was introduced in [2], where the authors proved that the space of such functions is a Banach Algebra. Moreover, they characterized also the Nemytskii operator acting in this space. Thus our result creates a continuation of the paper [2].
On the Hammerstein equation in the space of functions of bounded -variation in the plane
In this paper we study existence and uniqueness of solutions for the Hammerstein equation in the space of function of bounded total variation in the sense of Riesz, where , and are suitable functions.
Controllability of second-order equations in .
On second -variation
We present the notion of bounded second -variation for real functions defined on an interval . We introduce the class of all functions of bounded second -variation on . We show several properties of this class and present a sufficient condition under which a composition operator acts between these spaces.
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