Shape preserving approximation by real and complex polynomials gal sorin g anastassiou george a
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. Then, we prove that beginning with an index, these operators preserve the starlikeness, convexity and spirallikeness in the unit disk. Here we study the approximation properties e. Keywords Bernstein-Stancu operators, eigenvalues, eigenfunctions, iterates. In the present paper, we introduce a general class of positive operators of discrete type acting on the space of real valued functions defined on a plane domain. Also, we estimate the rate of convergence and the exact order of approximation.

The main topics are structured in four chapters, followed by an appendix: shape-preserving approximation and interpolation of real functions of one real variable by real polynomials; shape-preserving approximation of real functions of several real variables by multivariate real polynomials; shape-preserving approximation of analytic functions of one complex variable by complex polynomials in the unit disk; and shape-preserving approximation of analytic functions of several complex variables on the unit ball or the unit polydisk by polynomials of several complex variables. In this paper, we establish some theorems on approximation and Voronovskaja type results for complex modified Szász-Mirakjan-Stancu operators attached to analytic functions having exponential growth on compact disks. Shape-Preserving Approximation by Real and Complex Polynomials contains many open problems at the end of each chapter to stimulate future research along with a rich and updated bibliography surveying the vast literature. In the present article, we deal with the overconvergence of the Sz? The aim of this paper is to construct a decomposable measure on the class of measurable intuition. We also study the exact order of approximation. More important, our results show the overconvergence phenomenon for these complex operators.

More important, our results show the overconvergence phenomenon for these complex operators. In this paper, the order of simultaneous approximation and Voronovskaja kind results with quantitative estimate for the complex genuine Durrmeyer polynomials attached to analytic functions on compact disks are obtained. Such approximation methods are useful in many problems that arise in science and engineering and require an optimal mathematical representation of physical reality. In this paper we introduce a kind of complex summation-integral type operators and study the approximation properties of these operators. We obtain the order of simultaneous approximation and a Voronovskaja-type result with quantitative estimate for these complex Schurer-Stancu operators attached to analytic functions on compact disks.

First comprehensive treatment in book form of shape-preserving approximation by real or complex polynomials in one or several variables Of interest to grad students and researchers in approximation theory, mathematical analysis, numerical analysis, Computer Aided Geometric Design, robotics, data fitting, chemistry, fluid mechanics, and engineering Contains many open problems to spur future research Rich and updated bibliography. In the present note we prove convergence results for over-iterates of certain generalized Bernstein-Stancu operators. The exact order of simultaneous approximation and Voronovaskaja-type results with quantitative estimate for analytic functions in compact disks are obtained. However, our approach is different in the sense that it uses the spectrum of the operators involved. In the case of max-product Whittaker operator, for positive valued functions, essentially a better order of approximation is obtained. In the present paper, we introduce Stancu type Bernstein—Schurer polynomials and their Kantorovich variants.

In this paper, the order of simultaneous approximation and Voronovskaja-type results with quantitative estimate for complex Bernstein—Schurer and Kantorovich—Schurer polynomials attached to analytic functions on compact disks are obtained. In this way, we show the overconvergence phenomenon for these operators, namely the extensions of the approximation properties with quantitative estimates from the real intervals to compact disks in the complex plane. Based on the weakly Picard operators and the contraction principle, our aim is to study the convergence of the iterates of our defined operators. We obtain a Voronovskaja-type result with quantitative estimate for these operators attached to analytic functions on compact disks. In this way, we put in evidence the overconvergence phenomenon for the genuine Durrmeyer polynomials, namely the extensions of the approximation properties with quantitative estimates from real intervals to compact disks in the complex plane.

By considering well-known classical interpolation operators such as Lagrange, Grünwald, Hermite-Fejér and Shepard type, the study is mainly developed for the univariate and bivariate cases. The aim of this paper is to construct a decomposable measure on the class of measurable intuitionistic fuzzy sets, extending thus the corresponding result for fuzzy sets in a very recent paper. The main tool in this construction is a non-trivial approximation with restrictions result concerning the intuitionistic fuzzy sets. In such a way, we put in evidence the overconvergence phenomenon for the Sz? The text will be useful to graduate students and researchers interested in approximation theory, mathematical analysis, numerical analysis, computer aided geometric design, robotics, data fitting, chemistry, fluid mechanics, and engineering. Secondly, we study the approximation properties of the iterates of complex Bernstein polynomials and we prove that they preserve in the unit disk beginning with an index the univalence, starlikeness, convexity and spirallikeness. Master degree in Analysis in 1977, at the same university.

We introduce a class of complex Schurer-Stancu operators and study the approximation properties of these operators. Also, we discuss the exact order in simultaneous approximation by these operators and its derivatives and the asymptotic result with quantitative upper estimate. One of the first books on the subject, it presents to the reader, recent work featuring many new interesting results in this field, including an excellent survey of past research. This monograph presents the first comprehensive treatment in book form of shape-preserving approximation by real or complex polynomials in one or several variables. In this way, we put in evidence the overconvergence phenomenon for the Bernstein—Schurer polynomials, namely the extensions of approximation properties with quantitative estimates from real intervals to compact disks in the complex plane. Accompanied by numerous open problems, an updated set of references, and an appendix featuring illustrations of nine types of Shepard surfaces, this unique text is best suited to graduate students and researchers in mathematical analysis, interpolation of functions, pure and applied mathematicians in numerical analysis, approximation theory, data fitting, computer aided geometric design, fluid mechanics, and engineering researchers. Our results improve those of Anastassiou and Gal Comput Math Appl 58:734—743, 2009.

Also, some approximation properties of this process are revealed and concrete examples of our approach are given. The appendix treats related results of non-polynomial and non-spline approximations preserving shape including those by complexified operators with applications to complex partial differential equations. Our results show that extension of the complex genuine q-Bernstein-Durrmeyer polyno-mials from real intervals to compact disks in the complex plane extends approximation properties with quantitative estimates. . .

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