Approximation By Max Product Type Operators

Author : Barnabás Bede,Lucian Coroianu,Sorin G. Gal
Publisher : Springer
Page : 458 pages
File Size : 41,8 Mb
Release : 2016-08-08
Category : Mathematics
ISBN : 9783319341897

Get Book

Approximation by Max-Product Type Operators by Barnabás Bede,Lucian Coroianu,Sorin G. Gal Pdf

This monograph presents a broad treatment of developments in an area of constructive approximation involving the so-called "max-product" type operators. The exposition highlights the max-product operators as those which allow one to obtain, in many cases, more valuable estimates than those obtained by classical approaches. The text considers a wide variety of operators which are studied for a number of interesting problems such as quantitative estimates, convergence, saturation results, localization, to name several. Additionally, the book discusses the perfect analogies between the probabilistic approaches of the classical Bernstein type operators and of the classical convolution operators (non-periodic and periodic cases), and the possibilistic approaches of the max-product variants of these operators. These approaches allow for two natural interpretations of the max-product Bernstein type operators and convolution type operators: firstly, as possibilistic expectations of some fuzzy variables, and secondly, as bases for the Feller type scheme in terms of the possibilistic integral. These approaches also offer new proofs for the uniform convergence based on a Chebyshev type inequality in the theory of possibility. Researchers in the fields of approximation of functions, signal theory, approximation of fuzzy numbers, image processing, and numerical analysis will find this book most beneficial. This book is also a good reference for graduates and postgraduates taking courses in approximation theory.

Author : George A. Anastassiou
Publisher : Springer
Page : 293 pages
File Size : 40,9 Mb
Release : 2018-04-17
Category : Technology & Engineering
ISBN : 9783319895093

Get Book

Nonlinearity: Ordinary and Fractional Approximations by Sublinear and Max-Product Operators by George A. Anastassiou Pdf

This book focuses on approximations under the presence of ordinary and fractional smoothness, presenting both the univariate and multivariate cases. It also explores approximations under convexity and a new trend in approximation theory –approximation by sublinear operators with applications to max-product operators, which are nonlinear and rational providing very fast and flexible approximations. The results presented have applications in numerous areas of pure and applied mathematics, especially in approximation theory and numerical analysis in both ordinary and fractional senses. As such this book is suitable for researchers, graduate students, and seminars of the above disciplines, and is a must for all science and engineering libraries.

Author : Ioannis N. Parasidis,Efthimios Providas,Themistocles M. Rassias
Publisher : Springer Nature
Page : 1050 pages
File Size : 47,5 Mb
Release : 2022-03-10
Category : Mathematics
ISBN : 9783030847210

Get Book

Mathematical Analysis in Interdisciplinary Research by Ioannis N. Parasidis,Efthimios Providas,Themistocles M. Rassias Pdf

This contributed volume provides an extensive account of research and expository papers in a broad domain of mathematical analysis and its various applications to a multitude of fields. Presenting the state-of-the-art knowledge in a wide range of topics, the book will be useful to graduate students and researchers in theoretical and applicable interdisciplinary research. The focus is on several subjects including: optimal control problems, optimal maintenance of communication networks, optimal emergency evacuation with uncertainty, cooperative and noncooperative partial differential systems, variational inequalities and general equilibrium models, anisotropic elasticity and harmonic functions, nonlinear stochastic differential equations, operator equations, max-product operators of Kantorovich type, perturbations of operators, integral operators, dynamical systems involving maximal monotone operators, the three-body problem, deceptive systems, hyperbolic equations, strongly generalized preinvex functions, Dirichlet characters, probability distribution functions, applied statistics, integral inequalities, generalized convexity, global hyperbolicity of spacetimes, Douglas-Rachford methods, fixed point problems, the general Rodrigues problem, Banach algebras, affine group, Gibbs semigroup, relator spaces, sparse data representation, Meier-Keeler sequential contractions, hybrid contractions, and polynomial equations. Some of the works published within this volume provide as well guidelines for further research and proposals for new directions and open problems.

Author : Nicholas J. Daras,Themistocles M. Rassias
Publisher : Springer Nature
Page : 934 pages
File Size : 45,7 Mb
Release : 2022-05-05
Category : Mathematics
ISBN : 9783030841225

Get Book

Approximation and Computation in Science and Engineering by Nicholas J. Daras,Themistocles M. Rassias Pdf

In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume. It is addressed to graduate students, research mathematicians, physicists, and engineers. Individual contributions are devoted to topics of approximation theory, functional equations and inequalities, fixed point theory, numerical analysis, theory of wavelets, convex analysis, topology, operator theory, differential operators, fractional integral operators, integro-differential equations, ternary algebras, super and hyper relators, variational analysis, discrete mathematics, cryptography, and a variety of applications in interdisciplinary topics. Several of these domains have a strong connection with both theories and problems of linear and nonlinear optimization. The combination of results from various domains provides the reader with a solid, state-of-the-art interdisciplinary reference to theory and problems. Some of the works provide guidelines for further research and proposals for new directions and open problems with relevant discussions.

Author : Sorin G. Gal
Publisher : Springer Science & Business Media
Page : 359 pages
File Size : 54,6 Mb
Release : 2010-06-09
Category : Mathematics
ISBN : 9780817647032

Get Book

Shape-Preserving Approximation by Real and Complex Polynomials by Sorin G. Gal Pdf

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

Author : George A. Anastassiou
Publisher : Springer Nature
Page : 525 pages
File Size : 41,5 Mb
Release : 2020-01-15
Category : Technology & Engineering
ISBN : 9783030386368

Get Book

Intelligent Analysis: Fractional Inequalities and Approximations Expanded by George A. Anastassiou Pdf

This book focuses on computational and fractional analysis, two areas that are very important in their own right, and which are used in a broad variety of real-world applications. We start with the important Iyengar type inequalities and we continue with Choquet integral analytical inequalities, which are involved in major applications in economics. In turn, we address the local fractional derivatives of Riemann–Liouville type and related results including inequalities. We examine the case of low order Riemann–Liouville fractional derivatives and inequalities without initial conditions, together with related approximations. In the next section, we discuss quantitative complex approximation theory by operators and various important complex fractional inequalities. We also cover the conformable fractional approximation of Csiszar’s well-known f-divergence, and present conformable fractional self-adjoint operator inequalities. We continue by investigating new local fractional M-derivatives that share all the basic properties of ordinary derivatives. In closing, we discuss the new complex multivariate Taylor formula with integral remainder. Sharing results that can be applied in various areas of pure and applied mathematics, the book offers a valuable resource for researchers and graduate students, and can be used to support seminars in related fields.

Author : Stephen D. Casey,M. Maurice Dodson,Paulo J. S. G. Ferreira,Ahmed Zayed
Publisher : Springer Nature
Page : 580 pages
File Size : 48,8 Mb
Release : 2024-01-04
Category : Mathematics
ISBN : 9783031411304

Get Book

Sampling, Approximation, and Signal Analysis by Stephen D. Casey,M. Maurice Dodson,Paulo J. S. G. Ferreira,Ahmed Zayed Pdf

During his long and distinguished career, J. Rowland Higgins (1935-2020) made a substantial impact on many mathematical fields through his work on sampling theory, his deep knowledge of its history, and his service to the community. This volume is a tribute to his work and legacy, featuring chapters written by distinguished mathematicians that explore cutting-edge research in sampling, approximation, signal analysis, and other related areas. An introductory chapter provides a biography of Higgins that explores his rich and unique life, along with a bibliography of his papers; a brief history of the SampTA meetings – of which he was a Founding Member – is also included. The remaining articles are grouped into four sections – classical sampling, theoretical extensions, frame theory, and applications of sampling theory – and explore Higgins’ contributions to these areas, as well as some of the latest developments.

Author : R. N. Mohapatra,S. Yugesh,G. Kalpana,C. Kalaivani
Publisher : Springer Nature
Page : 661 pages
File Size : 49,7 Mb
Release : 2021-05-05
Category : Mathematics
ISBN : 9789813346468

Get Book

Mathematical Analysis and Computing by R. N. Mohapatra,S. Yugesh,G. Kalpana,C. Kalaivani Pdf

This book is a collection of selected papers presented at the International Conference on Mathematical Analysis and Computing (ICMAC 2019) held at Sri Sivasubramaniya Nadar College of Engineering, Chennai, India, from 23–24 December 2019. Having found its applications in game theory, economics, and operations research, mathematical analysis plays an important role in analyzing models of physical systems and provides a sound logical base for problems stated in a qualitative manner. This book aims at disseminating recent advances in areas of mathematical analysis, soft computing, approximation and optimization through original research articles and expository survey papers. This book will be of value to research scholars, professors, and industrialists working in these areas.

Author : George A. Anastassiou
Publisher : Springer Nature
Page : 523 pages
File Size : 48,5 Mb
Release : 2021-04-01
Category : Technology & Engineering
ISBN : 9783030714819

Get Book

Constructive Fractional Analysis with Applications by George A. Anastassiou Pdf

This book includes constructive approximation theory; it presents ordinary and fractional approximations by positive sublinear operators, and high order approximation by multivariate generalized Picard, Gauss–Weierstrass, Poisson–Cauchy and trigonometric singular integrals. Constructive and Computational Fractional Analysis recently is more and more in the center of mathematics because of their great applications in the real world. In this book, all presented is original work by the author given at a very general level to cover a maximum number of cases in various applications. The author applies generalized fractional differentiation techniques of Riemann–Liouville, Caputo and Canavati types and of fractional variable order to various kinds of inequalities such as of Opial, Hardy, Hilbert–Pachpatte and on the spherical shell. He continues with E. R. Love left- and right-side fractional integral inequalities. They follow fractional Landau inequalities, of left and right sides, univariate and multivariate, including ones for Semigroups. These are developed to all possible directions, and right-side multivariate fractional Taylor formulae are proven for the purpose. It continues with several Gronwall fractional inequalities of variable order. This book results are expected to find applications in many areas of pure and applied mathematics. As such this book is suitable for researchers, graduate students and seminars of the above disciplines, also to be in all science and engineering libraries.

Author : George A. Anastassiou
Publisher : Springer Nature
Page : 501 pages
File Size : 43,9 Mb
Release : 2020-11-25
Category : Technology & Engineering
ISBN : 9783030569624

Get Book

Generalized Fractional Calculus by George A. Anastassiou Pdf

This book applies generalized fractional differentiation techniques of Caputo, Canavati and Conformable types to a great variety of integral inequalities e.g. of Ostrowski and Opial types, etc. Some of these are extended to Banach space valued functions. These inequalities have also great impact in numerical analysis, stochastics and fractional differential equations. The book continues with generalized fractional approximations by positive sublinear operators which derive from the presented Korovkin type inequalities and also includes abstract cases. It presents also multivariate complex Korovkin quantitative approximation theory. It follows M-fractional integral inequalities of Ostrowski and Polya types. The results are weighted so they provide a great variety of cases and applications. The second part of the book deals with the quantitative fractional Korovkin type approximation of stochastic processes and lays there the foundations of stochastic fractional calculus. The book considers both Caputo and Conformable fractional directions and derives regular and trigonometric results. The positive linear operators can be expectation operator commutative or not. This book results are expected to find applications in many areas of pure and applied mathematics and stochastics. As such this monograph is suitable for researchers, graduate students, and seminars of the above disciplines, also to be in all science and engineering libraries.

Author : George A. Anastassiou,Oktay Duman
Publisher : Springer
Page : 502 pages
File Size : 46,6 Mb
Release : 2016-03-21
Category : Technology & Engineering
ISBN : 9783319303222

Get Book

Intelligent Mathematics II: Applied Mathematics and Approximation Theory by George A. Anastassiou,Oktay Duman Pdf

This special volume is a collection of outstanding more applied articles presented in AMAT 2015 held in Ankara, May 28-31, 2015, at TOBB Economics and Technology University. The collection is suitable for Applied and Computational Mathematics and Engineering practitioners, also for related graduate students and researchers. Furthermore it will be a useful resource for all science and engineering libraries. This book includes 29 self-contained and well-edited chapters that can be among others useful for seminars in applied and computational mathematics, as well as in engineering.

Author : George A. Anastassiou
Publisher : Springer Science & Business Media
Page : 793 pages
File Size : 52,8 Mb
Release : 2011-03-19
Category : Technology & Engineering
ISBN : 9783642170980

Get Book

Intelligent Mathematics: Computational Analysis by George A. Anastassiou Pdf

Knowledge can be modeled and computed using computational mathematical methods, then lead to real world conclusions. The strongly related to that Computational Analysis is a very large area with lots of applications. This monograph includes a great variety of topics of Computational Analysis. We present: probabilistic wavelet approximations, constrained abstract approximation theory, shape preserving weighted approximation, non positive approximations to definite integrals, discrete best approximation, approximation theory of general Picard singular operators including global smoothness preservation property, fractional singular operators. We also deal with non-isotropic general Picard singular multivariate operators and q-Gauss-Weierstrass singular q-integral operators. We talk about quantitative approximations by shift-invariant univariate and multivariate integral operators, nonlinear neural networks approximation, convergence with rates of positive linear operators, quantitative approximation by bounded linear operators, univariate and multivariate quantitative approximation by stochastic positive linear operators on univariate and multivariate stochastic processes. We further present right fractional calculus and give quantitative fractional Korovkin theory of positive linear operators. We also give analytical inequalities, fractional Opial inequalities, fractional identities and inequalities regarding fractional integrals. We further deal with semi group operator approximation, simultaneous Feller probabilistic approximation. We also present Fuzzy singular operator approximations. We give transfers from real to fuzzy approximation and talk about fuzzy wavelet and fuzzy neural networks approximations, fuzzy fractional calculus and fuzzy Ostrowski inequality. We talk about discrete fractional calculus, nabla discrete fractional calculus and inequalities. We study the q-inequalities, and q-fractional inequalities. We further study time scales: delta and nabla approaches, duality principle and inequalities. We introduce delta and nabla time scales fractional calculus and inequalities. We finally study convergence with rates of approximate solutions to exact solution of multivariate Dirichlet problem and multivariate heat equation, and discuss the uniqueness of solution of general evolution partial differential equation \ in multivariate time. The exposed results are expected to find applications to: applied and computational mathematics, stochastics, engineering, artificial intelligence, vision, complexity and machine learning. This monograph is suitable for graduate students and researchers.

Author : Osvaldo Gervasi,Beniamino Murgante,Sanjay Misra,Elena Stankova,Carmelo M. Torre,Ana Maria A.C. Rocha,David Taniar,Bernady O. Apduhan,Eufemia Tarantino,Yeonseung Ryu
Publisher : Springer
Page : 754 pages
File Size : 46,7 Mb
Release : 2018-07-03
Category : Computers
ISBN : 9783319951621

Get Book

Computational Science and Its Applications – ICCSA 2018 by Osvaldo Gervasi,Beniamino Murgante,Sanjay Misra,Elena Stankova,Carmelo M. Torre,Ana Maria A.C. Rocha,David Taniar,Bernady O. Apduhan,Eufemia Tarantino,Yeonseung Ryu Pdf

The five volume set LNCS 10960 until 10964 constitutes the refereed proceedings of the 18th International Conference on Computational Science and Its Applications, ICCSA 2018, held in Melbourne, Australia, in July 2018. Apart from the general tracks, ICCSA 2018 also includes 34 international workshops in various areas of computational sciences, ranging from computational science technologies, to specific areas of computational sciences, such as computer graphics and virtual reality. The total of 265 full papers and 10 short papers presented in the 5-volume proceedings set of ICCSA 2018, were carefully reviewed and selected from 892 submissions.

Author : Universitatea "Babeș-Bolyai."
Publisher : Unknown
Page : 766 pages
File Size : 48,7 Mb
Release : 2011
Category : Mathematics
ISBN : UCBK:C083614221

Get Book

Studia Universitatis Babeș-Bolyai by Universitatea "Babeș-Bolyai." Pdf

Author : George A. Anastassiou
Publisher : Unknown
Page : 128 pages
File Size : 41,6 Mb
Release : 2018
Category : Approximation theory
ISBN : 3319895109

Get Book

Nonlinearity by George A. Anastassiou Pdf

This book focuses on approximations under the presence of ordinary and fractional smoothness, presenting both the univariate and multivariate cases. It also explores approximations under convexity and a new trend in approximation theory -approximation by sublinear operators with applications to max-product operators, which are nonlinear and rational providing very fast and flexible approximations. The results presented have applications in numerous areas of pure and applied mathematics, especially in approximation theory and numerical analysis in both ordinary and fractional senses. As such this book is suitable for researchers, graduate students, and seminars of the above disciplines, and is a must for all science and engineering libraries.