Papers by José A Guerrero
Publicationes Mathematicae Debrecen
We sonsider the Nemytskii operator, i.e. the composition operator defined by (N u) (t) = H(t, u(t... more We sonsider the Nemytskii operator, i.e. the composition operator defined by (N u) (t) = H(t, u(t)), where H is a given set-valued function. It is shown that if the operator N maps the space of set-valued functions of bounded p-variation in the sense of Riesz into the space of set-valued functions of bounded q-variation in the sense of Riesz, there is 1 ≤ q ≤ p < ∞, and if it is globally Lipschitzian, then it has to be of the form (N u) (t) = A(t)u(t) + B(t), where A(t) are linear continuous set-valued and B is a set-valued function of bounded q-variation in the sense of Riesz. This generalizes results of G. Zawadzka [8], A
Bulletin of the Korean Mathematical Society, 2013
We prove, under some general assumptions, that a generator of any uniformly bounded Nemytskij ope... more We prove, under some general assumptions, that a generator of any uniformly bounded Nemytskij operator, mapping a subset of space of functions of bounded variation in the sense of Wiener-Young into another space of this type, must be an affine function with respect to the second variable.
Advances in Pure Mathematics, 2016
We give a neccesary and sufficient condition on a function : f → such that the composition op... more We give a neccesary and sufficient condition on a function : f → such that the composition operator (Nemytskij Operator) H defined by Hf f h = acts in the space ( ) [ ] ( ) , p WBV a b ⋅ and satisfies a local Lipschitz condition. And, we prove that every locally defined operator mapping the space of continuous and bounded Wiener ( ) p ⋅ -variation with variable exponent functions into itself is a Nemytskij com- position operator.
Journal of Mathematics, 2015
We study the locally defined operator on the spaces of bounded Rieszp-variation functions and we ... more We study the locally defined operator on the spaces of bounded Rieszp-variation functions and we prove that those operators are the Nemytskii operator.
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, 2016
suitable functions. The existence and uniqueness of solutions are proved by means of the Leray-Sc... more suitable functions. The existence and uniqueness of solutions are proved by means of the Leray-Schauder nonlinear alternative and the Banach contraction mapping principle.
Bulletin of the Korean Mathematical Society, 2015
The space BV 2 α (I) of all the real functions defined on interval I = [a, b] ⊂ R, which are of b... more The space BV 2 α (I) of all the real functions defined on interval I = [a, b] ⊂ R, which are of bounded second α-variation (in the sense De la Vallé Poussin) on I forms a Banach space. In this space we define an operator of substitution H generated by a function h : I × R −→ R, and prove, in particular, that if H maps BV 2 α (I) into itself and is globally Lipschitz or uniformly continuous, then h is an affine function with respect to the second variable.
Journal of Applied Mathematics and Computational Mechanics, 2015
We show that the one-sided regularizations of the generator of any uniformly bounded set-valued N... more We show that the one-sided regularizations of the generator of any uniformly bounded set-valued Nemytskij composition operator mapping the space of bounded variation functions in the sense of Wiener into the space of bounded variation functions with closed bounded convex values (in the sense of Wiener) are affine functions.
Bulletin of the Polish Academy of Sciences Mathematics, 2010
We show that the one-sided regularizations of the generator of any uniformly continuous and conve... more We show that the one-sided regularizations of the generator of any uniformly continuous and convex compact valued composition operator, acting in the spaces of functions of bounded variation in the sense of Wiener, is an affine function.
Nonlinear Analysis: Theory, Methods & Applications, 2011
Assume that the generator of a Nemytskii composition operator is a function of three variables: t... more Assume that the generator of a Nemytskii composition operator is a function of three variables: the first two real and third in a closed convex subset of a normed space, with values in a real Banach space. We prove that if this operator maps a certain subset of the Banach space of functions of two real variables of bounded Wiener ϕ-variation into another Banach space of a similar type, and is uniformly continuous, then the one-sided regularizations of the generator are affine in the third variable.
El impacto generado por el COVID-19, dio apertura a escenarios para la discusión sobre las formas... more El impacto generado por el COVID-19, dio apertura a escenarios para la discusión sobre las formas de aprehender en el proceso de enseñanza y aprendizaje desde la modalidad virtual, permitiendo una adecuación del entorno a fin de responder a desafíos actuales. Para ello, se planteó como objetivo determinar el impacto de la modalidad virtual respecto a la presencial ocasionada por el COVID-19, en las áreas de Formación Matemática y Educación Física del ISFODOSU, Recinto Luis Napoleón Núñez Molina. El método corresponde al paradigma cuantitativo, bajo la investigación de campo, de carácter descriptivo. En los resultados se encontró una percepción negativa por parte de los estudiantes sobre el nivel de competencias alcanzadas y aprendizaje significativo, en la modalidad virtual con respecto a la presencial, aun cuando se manejaron apropiadamente las herramientas de enseñanza y aprendizaje; sin embargo, están de acuerdo con el uso de la modalidad virtual en tiempos de pandemia.
In this paper we prove that if a uniformly bounded the nonlinear composition operator maps a subs... more In this paper we prove that if a uniformly bounded the nonlinear composition operator maps a subset of the space of functions of bounded total φ-bidimensional variation with weight function in the sense of Riesz, into another space of that type (with the same weight function), then the generator function of the operator is an affine function in the third variable. This extends previous results (see [1, 5, 9, 10]) in the one and two-dimensional setting.
Axioms, 2017
Since Lotfi A. Zadeh introduced the concept of fuzzy sets in 1965, many authors have devoted thei... more Since Lotfi A. Zadeh introduced the concept of fuzzy sets in 1965, many authors have devoted their efforts to the study of these new sets, both from a theoretical and applied point of view. Fuzzy sets were later extended in order to get more adequate and flexible models of inference processes, where uncertainty, imprecision or vagueness is present. Type 2 fuzzy sets comprise one of such extensions. In this paper, we introduce and study an extension of the fuzzy numbers (type 1), the type 2 generalized fuzzy numbers and type 2 fuzzy numbers. Moreover, we also define a partial order on these sets, which extends into these sets the usual order on real numbers, which undoubtedly becomes a new option to be taken into account in the existing total preorders for ranking interval type 2 fuzzy numbers, which are a subset of type 2 generalized fuzzy numbers.
Tatra Mountains Mathematical Publications, 2015
In this paper we present the concept of total κ-variation in the sense of Hardy-Vitali-Korenblum ... more In this paper we present the concept of total κ-variation in the sense of Hardy-Vitali-Korenblum for a real function defined in the rectangle I b a ⊂ R 2. We show that the space κBV (I b a , R) of real functions of two variables with finite total κ-variation is a Banach space endowed with the norm ||f || κ = |f (a)| + κT V (f, I b a). Also, we characterize the Nemytskij composition operator H that maps the space of functions of two real variables of bounded κ-variation κBV (I b a , R) into another space of a similar type and is uniformly bounded (or Lipschitzian or uniformly continuous).
Uniformly Bounded Composition Operators on the Space of Bounded Variation Functions in the Sense of Waterman
Mediterranean Journal of Mathematics, 2016
In this paper, we demonstrate under some general assumptions, that a generator of any uniformly b... more In this paper, we demonstrate under some general assumptions, that a generator of any uniformly bounded composition operator, mapping spaces of bounded variation (Waterman) functions into other spaces of this type, must be an affine function in the functional variable.
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Papers by José A Guerrero