Approximation By Complex Bernstein And Convolution Type Operators
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Approximation By Complex Bernstein And Convolution Type Operators
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Author : Sorin G Gal
language : en
Publisher: World Scientific
Release Date : 2009-08-11
Approximation By Complex Bernstein And Convolution Type Operators written by Sorin G Gal and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-11 with Mathematics categories.
The monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals. The operators studied are of the following types: Bernstein, Bernstein—Faber, Bernstein-Butzer, q-Bernstein, Bernstein-Stancu, Bernstein-Kantorovich, Favard-Szász-Mirakjan, Baskakov and Balázs-Szabados.The second main objective is to provide a study of the approximation and geometric properties of several types of complex convolutions: the de la Vallée Poussin, Fejér, Riesz-Zygmund, Jackson, Rogosinski, Picard, Poisson-Cauchy, Gauss-Weierstrass, q-Picard, q-Gauss-Weierstrass, Post-Widder, rotation-invariant, Sikkema and nonlinear. Several applications to partial differential equations (PDEs) are also presented.Many of the open problems encountered in the studies are proposed at the end of each chapter. For further research, the monograph suggests and advocates similar studies for other complex Bernstein-type operators, and for other linear and nonlinear convolutions.
Approximation By Complex Bernstein And Convolution Type Operators
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Author : Sorin G. Gal
language : en
Publisher: World Scientific Publishing Company
Release Date : 2009
Approximation By Complex Bernstein And Convolution Type Operators written by Sorin G. Gal and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with MATHEMATICS categories.
The monograph, As its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, To extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals. The operators studied are of the following types: Bernstein, Bernstein–Faber, Bernstein–Butzer, q-Bernstein, Bernstein–Stancu, Bernstein–Kantorovich, Favard–SzÁsz–Mirakjan, Baskakov and BalÁzs–Szabados. The second main objective is to provide a study of the approximation and geometric properties of several types of complex convolutions: The de la VallÉe Poussin, FejÉr, Riesz-Zygmund, Jackson, Rogosinski, Picard, Poisson–Cauchy, Gauss–Weierstrass, q-Picard, q-Gauss–Weierstrass, Post–Widder, rotation-invariant, Sikkema and nonlinear. Several applications to partial differential equations (PDEs) are also presented. Many of the open problems encountered in the studies are proposed at the end of each chapter. For further research, The monograph suggests and advocates similar studies for other complex Bernstein-type operators, and for other linear and nonlinear convolutions.
Approximation With Positive Linear Operators And Linear Combinations
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Author : Vijay Gupta
language : en
Publisher: Springer
Release Date : 2017-06-27
Approximation With Positive Linear Operators And Linear Combinations written by Vijay Gupta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-27 with Mathematics categories.
This book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation. Fundamental and recent results from the past decade are described with their corresponding proofs. The volume consists of eight chapters that provide detailed insight into the representation of monomials of the operators Ln , direct and inverse estimates for a broad class of positive linear operators, and case studies involving finite and unbounded intervals of real and complex functions. Strong converse inequalities of Type A in terminology of Ditzian–Ivanov for linear combinations of Bernstein and Bernstein–Kantorovich operators and various Voronovskaja-type estimates for some linear combinations are analyzed and explained. Graduate students and researchers in approximation theory will find the list of open problems in approximation of linear combinations useful. The book serves as a reference for graduate and postgraduate courses as well as a basis for future study and development.
Bernstein Operators And Their Properties
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Author : Jorge Bustamante
language : en
Publisher: Birkhäuser
Release Date : 2017-04-13
Bernstein Operators And Their Properties written by Jorge Bustamante and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-13 with Mathematics categories.
This book provides comprehensive information on the main aspects of Bernstein operators, based on the literature to date. Bernstein operators have a long-standing history and many papers have been written on them. Among all types of positive linear operators, they occupy a unique position because of their elegance and notable approximation properties. This book presents carefully selected material from the vast body of literature on this topic. In addition, it highlights new material, including several results (with proofs) appearing in a book for the first time. To facilitate comprehension, exercises are included at the end of each chapter. The book is largely self-contained and the methods in the proofs are kept as straightforward as possible. Further, it requires only a basic grasp of analysis, making it a valuable and appealing resource for advanced graduate students and researchers alike.
Applications Of Q Calculus In Operator Theory
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Author : Ali Aral
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-05-09
Applications Of Q Calculus In Operator Theory written by Ali Aral and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-09 with Mathematics categories.
The approximation of functions by linear positive operators is an important research topic in general mathematics and it also provides powerful tools to application areas such as computer-aided geometric design, numerical analysis, and solutions of differential equations. q-Calculus is a generalization of many subjects, such as hypergeometric series, complex analysis, and particle physics. This monograph is an introduction to combining approximation theory and q-Calculus with applications, by using well- known operators. The presentation is systematic and the authors include a brief summary of the notations and basic definitions of q-calculus before delving into more advanced material. The many applications of q-calculus in the theory of approximation, especially on various operators, which includes convergence of operators to functions in real and complex domain forms the gist of the book. This book is suitable for researchers and students in mathematics, physics and engineering, and for professionals who would enjoy exploring the host of mathematical techniques and ideas that are collected and discussed in the book.
Advanced Mathematics For The Modeling And Solution Of Challenging Problems In Engineering
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Author : Oscar Castillo
language : en
Publisher: Springer Nature
Release Date : 2025-06-01
Advanced Mathematics For The Modeling And Solution Of Challenging Problems In Engineering written by Oscar Castillo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-01 with Technology & Engineering categories.
This book includes studies that give mathematical solution methods and mathematical modeling to support these methods for solving problems in the current application area of engineering, as well as studies that include solutions for problems that are also related to current life areas. In this book, some current problems in the field of mathematics and engineering, solutions to solve these problems and existing engineering methods for these problems are included. Basically, machinery, chemistry, electronics, computers, construction, environment, etc. studies in both the application and theoretical fields of mathematics are needed to solve optimization, modeling, encryption methods and thermal problems that are currently encountered in engineering fields. In this book, some current problems are presented and related theoretical and applied mathematical studies are included.
Mathematics Without Boundaries
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Author : Panos M. Pardalos
language : en
Publisher: Springer
Release Date : 2014-09-16
Mathematics Without Boundaries written by Panos M. Pardalos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-16 with Mathematics categories.
This volume consists of chapters written by eminent scientists and engineers from the international community and present significant advances in several theories, methods and applications of an interdisciplinary research. These contributions focus on both old and recent developments of Global Optimization Theory, Convex Analysis, Calculus of Variations, Discrete Mathematics and Geometry, as well as several applications to a large variety of concrete problems, including applications of computers to the study of smoothness and analyticity of functions, applications to epidemiological diffusion, networks, mathematical models of elastic and piezoelectric fields, optimal algorithms, stability of neutral type vector functional differential equations, sampling and rational interpolation for non-band-limited signals, recurrent neural network for convex optimization problems and experimental design. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical and Engineering subjects and especially to graduate students who search for the latest information.
Handbook Of Functional Equations
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Author : Themistocles M. Rassias
language : en
Publisher: Springer
Release Date : 2014-11-18
Handbook Of Functional Equations written by Themistocles M. Rassias and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-18 with Mathematics categories.
As Richard Bellman has so elegantly stated at the Second International Conference on General Inequalities (Oberwolfach, 1978), “There are three reasons for the study of inequalities: practical, theoretical, and aesthetic.” On the aesthetic aspects, he said, “As has been pointed out, beauty is in the eye of the beholder. However, it is generally agreed that certain pieces of music, art, or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive.” The content of the Handbook focuses mainly on both old and recent developments on approximate homomorphisms, on a relation between the Hardy–Hilbert and the Gabriel inequality, generalized Hardy–Hilbert type inequalities on multiple weighted Orlicz spaces, half-discrete Hilbert-type inequalities, on affine mappings, on contractive operators, on multiplicative Ostrowski and trapezoid inequalities, Ostrowski type inequalities for the Riemann–Stieltjes integral, means and related functional inequalities, Weighted Gini means, controlled additive relations, Szasz–Mirakyan operators, extremal problems in polynomials and entire functions, applications of functional equations to Dirichlet problem for doubly connected domains, nonlinear elliptic problems depending on parameters, on strongly convex functions, as well as applications to some new algorithms for solving general equilibrium problems, inequalities for the Fisher’s information measures, financial networks, mathematical models of mechanical fields in media with inclusions and holes.
Quaternionic Approximation
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Author : Sorin G. Gal
language : en
Publisher: Springer
Release Date : 2019-04-12
Quaternionic Approximation written by Sorin G. Gal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-12 with Mathematics categories.
This book presents the extensions to the quaternionic setting of some of the main approximation results in complex analysis. It also includes the main inequalities regarding the behavior of the derivatives of polynomials with quaternionic cofficients. With some few exceptions, all the material in this book belongs to recent research of the authors on the approximation of slice regular functions of a quaternionic variable. The book is addressed to researchers in various areas of mathematical analysis, in particular hypercomplex analysis, and approximation theory. It is accessible to graduate students and suitable for graduate courses in the above framework.
Differential Sheaves And Connections A Natural Approach To Physical Geometry
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Author : Anastasios Mallios
language : en
Publisher: World Scientific
Release Date : 2015-09-17
Differential Sheaves And Connections A Natural Approach To Physical Geometry written by Anastasios Mallios and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-17 with Mathematics categories.
This unique book provides a self-contained conceptual and technical introduction to the theory of differential sheaves. This serves both the newcomer and the experienced researcher in undertaking a background-independent, natural and relational approach to 'physical geometry'. In this manner, this book is situated at the crossroads between the foundations of mathematical analysis with a view toward differential geometry and the foundations of theoretical physics with a view toward quantum mechanics and quantum gravity. The unifying thread is provided by the theory of adjoint functors in category theory and the elucidation of the concepts of sheaf theory and homological algebra in relation to the description and analysis of dynamically constituted physical geometric spectrums.