Papers by Antonio Jesús López Moreno
Filomat, 2021
The present paper deals with the approximation properties for exponential functions of general Du... more The present paper deals with the approximation properties for exponential functions of general Durrmeyer type operators having the weights of Sz?sz basis functions. Here we give explicit expressions for exponential type moments by means of which we establish, for the derivatives of the operators, the Voronovskaja formulas for functions of exponential growth and the corresponding weighted quantitative estimates for the remainder in simultaneous approximation.
Journal of Mathematical Analysis and Applications, 2011
In this paper we study localization results for classical sequences of linear positive operators ... more In this paper we study localization results for classical sequences of linear positive operators that are particular cases of the generalized Baskakov/Mastroianni operators and also for certain class of composite operators that can be derived from them by means of a suitable transformation. Amongst these composite operators we can find classical sequences like the Meyer-König and Zeller operators and the Bleimann, Butzer and Hahn ones. We extend in different senses the traditional form of the localization results that we find in the classical literature and we show several examples of sequences with different behavior to this respect.
Applied Mathematics and Computation, 2009
The present paper deals with the study of the rate of convergence of the Bézier variant of certai... more The present paper deals with the study of the rate of convergence of the Bézier variant of certain Bernstein Durrmeyer type operators in simultaneous approximation.
Journal of Computational and Applied Mathematics, 2003
In this paper, we study the asymptotic expansion of the partial derivatives of a sequence of line... more In this paper, we study the asymptotic expansion of the partial derivatives of a sequence of linear conservative operators. We ÿnd su cient conditions on the sequence that guarantee that such an expansion can be derived from the asymptotic formula for the nondi erentiated sequence. Our results are valid even if the operators of the sequence present di cult conservative properties di erent form the classical preservation of the usual convexities. We use our theorems to obtain the complete asymptotic expansions and Voronovskaja formulae for the partial derivatives of multivariate versions of the Meyer-K onig and Zeller operators and the Bleimann, Butzer and Hahn operators.
A note on simultaneous approximation of functions
Given a sequence of natural numbers {m(n)} n=1 ∞ , m(n)≤n (n∈ℕ), and a function f∈C (s) [0,1], th... more Given a sequence of natural numbers {m(n)} n=1 ∞ , m(n)≤n (n∈ℕ), and a function f∈C (s) [0,1], the paper deals with the simultaneous approximation of f and its derivatives, on certain compact subsets of [0,1], by using the polynomials P n (f)=∑ k=m(n) n f(k/n)n kx k (1-x) n-k and P ˜ n (f)=∑ k=m(n) n f(k/n)n kx k (1-x) n-k · Specifically, the following Müntz-type results are proved: a) If limsup n→∞ m(n) n=c<1, then P n (f) and P ˜ n (f) converge to f in the usual norm of C (s) [a,b] whenever 1-2 -1/(1-c) <a<b<1· b) If limsup n→∞ m(n)log 2 n n=c<1, then P n (f) and P ˜ n (f) converge to f in the usual norm of C (s) [a,b] whenever 1-2 -c <a<b<1· The paper also contains final remarks concerning the approximation of a multivariate function f and its partial derivatives by natural extensions of P n (f) and P ˜ n (f). Finally, some open problems are stated.
Journal of Mathematical Analysis and Applications, 2007
In this paper we give a new proof of a classical result by Fréchet [M. Fréchet, Une définition fo... more In this paper we give a new proof of a classical result by Fréchet [M. Fréchet, Une définition fonctionnelle des polynomes, Nouv. Ann. 9 (4) (1909) 145-162]. Concretely, we prove that, if Δ k+1 h f = 0 and f is continuous at some point or bounded at some nonempty open set, then f ∈ P k. Moreover, as a consequence of the technique developed for our proof, it is possible to give a description of the closure of the graph for the solutions of the equation. Finally, we characterize some spaces of polynomials of several variables by the use of adequate generalizations of the forward differences operator Δ k+1 h .
International Journal of Mathematics and Mathematical Sciences, 2005
We prove the existence of a dense subsetΔof[0,4]such that for allα∈Δthere exists a subgroupXαof i... more We prove the existence of a dense subsetΔof[0,4]such that for allα∈Δthere exists a subgroupXαof infinite rank ofℤ[z]such thatXαis a discrete subgroup ofC[0,β]for allβ≥αbut it is not a discrete subgroup ofC[0,β]for anyβ∈(0,α).Given a set of nonnegative real numbersΛ={λi}i=0∞, aΛ-polynomial (or Müntz polynomial) is a function of the formp(x)=∑i=0naizλi(n∈ℕ). We denote byΠ(Λ)the space ofΛ-polynomials and byΠℤ(Λ):={p(x)=∑i=0naizλi∈Π(λ):ai∈ℤ for all i≥0}the set of integralΛ-polynomials. Clearly, the setsΠℤ(Λ)are subgroups of infinite rank ofℤ[x]wheneverΛ⊂ℕ,#Λ=∞(by infinite rank, we mean that the real vector space spanned byXdoes not have finite dimension. In all what follows we are uniquely interested in groups of infinite rank). Now, it is well known that the problem of approximation of functions on intervals[a,b]by polynomials with integral coefficients is solvable only for intervals[a,b]of length smaller than four and functionsfwhich are interpolable by polynomials ofℤ[x]on a certain ...
In this note, we give several definitions of metric corona properties which could be of interest ... more In this note, we give several definitions of metric corona properties which could be of interest in Set Topology, Functional Analysis and Approximation Theory, and prove that there are complete metrizable t.v.s. which are nice in the sense that they have a metric which is invariant by translations, but they do not have good corona properties. All classical function spaces satisfy good corona properties but it is an open question to know if this also holds for the more general setting of locally convex t.v.s.
A Muntz-type Theorem for Diophantine Approximation on Intervals of Length Smaller than Four
In this note we study the following question: Under which minimal assumptions on the function f i... more In this note we study the following question: Under which minimal assumptions on the function f is it true that the condition (∆ N +1 h f)(a) = 0 for all a ∈ R and h ≥ 0 implies that f is a polynomial of degree less than or equal to N ?
Filomat, 2018
In this paper we present a modification of the Phillips operators which reproduces the functions ... more In this paper we present a modification of the Phillips operators which reproduces the functions eat, ebt, a,b ? R. We study the moments and basic approximation properties for these new operators. For this purpose we adapt several already known result to the particular features of the new sequence that we propose here.
We present estimates on the rate of convergence for functions deened over multidimensional domain... more We present estimates on the rate of convergence for functions deened over multidimensional domains and their derivatives by linear positive operators involving the second order modulus of continuity. These results are applied to Bernstein type operators.
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Papers by Antonio Jesús López Moreno