Operator Methods in Approximation Theory

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On Sequences of J. P. King-Type Operators

This survey is devoted to a series of investigations developed in the last fifteen years, starting from the introduction of a sequence of positive linear operators which modify the classical Bernstein operators in order to reproduce constant functions and x2 on [0,1]. Nowadays, these operators are known as King operators, in honor of J. P. King who defined them, and they have been a source of inspiration for many scholars. In this paper we try to take stock of the situation and highlight the state of the art, hoping that this will be a useful tool for all people who intend to extend King's approach to some new contents within Approximation Theory. In particular, we recall the main results concerning certain King-type modifications of two well known sequences of positive linear operators, the Bernstein operators and the Szász-Mirakyan operators

O31 Integrative analysis reveals a molecular stratification of systemic autoimmune diseases

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Optimal Simultaneous Approximation via -Summability

We present optimal convergence results for the mth derivative of a function by sequences of linear operators. The usual convergence is replaced by -summability, with being a sequence of infinite matrices with nonnegative real entries, and the operators are assumed to be m-convex. Saturation results for nonconvergent but almost convergent sequences of operators are stated as corollaries

BERNSTEIN-TYPE OPERATORS THAT REPRODUCE EXPONENTIAL FUNCTIONS

Cardenas-Morales, Daniel/0000-0003-1038-3116WOS: 000445366500019In this paper we recover a generalization of the classical Bernstein operators introduced by Morigi and Neamtu in 2000. Specifically, we focus on a sequence of operators that reproduce the exponential functions exp(mu t) and exp(2 mu t), mu > 0. We study its convergence, this including qualitative and quantitative theorems, an asymptotic formula and saturation results. We also show their shape preserving properties by considering generalized convexity. Finally, a comparison is stated, that shows that in a certain sense and for certain family of illustrative functions the new sequence approximates better than the classical Bernstein polynomials.Research Projects DGA [E-64]; FEDER fundsEuropean Union (EU); Junta de Andalucia Research GroupJunta de Andalucia [FQM-0178]; [MTM2015-67006-P]The second author is partially supported by Research Projects DGA (E-64), MTM2015-67006-P, by FEDER funds, and by Junta de Andalucia Research Group FQM-0178

Szasz-Mirakyan Type Operators Which Fix Exponentials

Acar, Tuncer/0000-0003-0982-9459; Cardenas-Morales, Daniel/0000-0003-1038-3116WOS: 000414940700024In this paper, we construct a new general class of operators which have the classical Szasz Mirakyan ones as a basis, and fix the functions and with . The convergence of the corresponding sequences is discussed in exponential weighted spaces, and a Voronovskaya type result is given. Also we define a new weighted modulus of smoothness and determine the approximation order of the constructed operators. Finally, we study the goodness of the estimates of our new operators via saturation results.Kirikkale University, BAP (Turkey) [2017/014]; DGA (Spain) [E-64, MTM2015-67006-P]The first author is partially supported by Research Project of Kirikkale University, BAP, 2017/014 (Turkey). The third author is partially supported by Research Projects DGA (E-64), MTM2015-67006-P (Spain)

Voronovskaya type results for Bernstein-Chlodovsky operators preserving e2xe^{2x}

In this paper we continue the study of certain Bernstein-Chlodovsky operators B_n^∗ preserving the exponential function e^{2x} (x ≥0), recently introduced in [4]. In particular, we prove some Voronovskaya type theorems and we deduce some properties of the B_n^∗’s, such as saturation results. We also compare this new class of operators with the classical Bernstein-Chlodovsky ones, proving that the operators B_^∗ provide better approximation results for certain functions

On Bernstein-Chlodovsky operators preserving e2xe^{2x}

In this paper we introduce a generalization of Bernstein-Chlodovsky operators that preserves the exponential function $e^{2x}$ ($x geq 0$). We study its approximation properties in several function spaces, and we evaluate the rate of convergence by means of suitable moduli of con- tinuity. Throughout some estimates of the rate of convergence, we prove better error estimation than the original operators on certain intervals

Percutaneous Radiology Gastrostomy (PRG)-Associated Complications at a Tertiary Hospital over the Last 25 Years

Objectives: We aimed to describe and compare the complications associated with different percutaneous radiologic gastrostomy (PRG) techniques. Methods: A retrospective and prospective observational study was conducted. Patients who underwent a PRG between 1995–2020 were included. Techniques: A pigtail catheter was used until 2003, a balloon catheter without pexy was used between 2003–2009 and a balloon catheter with gastropexy was used between 2015–2021. For the comparison of proportions, X2 tests or Fisher’s test were used when necessary. Univariate analysis was performed to study the risk factors for PRG-associated complications. Results: n = 330 (pigtail = 114, balloon-type without pexy = 28, balloon-type with pexy = 188). The most frequent indication was head and neck cancer. The number of patients with complications was 44 (38.5%), 11 (39.2%) and 54 (28,7%), respectively. There were seven (25%) cases of peritonitis in the balloon-type without-pexy group and 1 (0.5%) in the balloon-type with-pexy group, the latter being the only patient who died in the total number of patients (0.3%). Two (1%) patients of the balloon-type with-pexy group presented with gastrocolic fistula. The rest of the complications were minor. Conclusions: The most frequent complications associated with the administration of enteral nutrition through PRG were minor and the implementation of the balloon-type technique with pexy has led to a decrease in them