Ulam Type Stability

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Ulam Type Stability

Author : Janusz Brzdęk
Publisher : Springer Nature
ISBN 13 : 3030289729
Total Pages : 514 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Ulam Type Stability by : Janusz Brzdęk

Download or read book Ulam Type Stability written by Janusz Brzdęk and published by Springer Nature. This book was released on 2019-10-29 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an outcome of two Conferences on Ulam Type Stability (CUTS) organized in 2016 (July 4-9, Cluj-Napoca, Romania) and in 2018 (October 8-13, 2018, Timisoara, Romania). It presents up-to-date insightful perspective and very resent research results on Ulam type stability of various classes of linear and nonlinear operators; in particular on the stability of many functional equations in a single and several variables (also in the lattice environments, Orlicz spaces, quasi-b-Banach spaces, and 2-Banach spaces) and some orthogonality relations (e.g., of Birkhoff–James). A variety of approaches are presented, but a particular emphasis is given to that of fixed points, with some new fixed point results and their applications provided. Besides these several other topics are considered that are somehow related to the Ulam stability such as: invariant means, geometry of Banach function modules, queueing systems, semi-inner products and parapreseminorms, subdominant eigenvalue location of a bordered diagonal matrix and optimal forward contract design for inventory. New directions and several open problems regarding stability and non-stability concepts are included. Ideal for use as a reference or in a seminar, this book is aimed toward graduate students, scientists and engineers working in functional equations, difference equations, operator theory, functional analysis, approximation theory, optimization theory, and fixed point theory who wish to be introduced to a wide spectrum of relevant theories, methods and applications leading to interdisciplinary research. It advances the possibilities for future research through an extensive bibliography and a large spectrum of techniques, methods and applications.

Ulam Stability of Operators

Author : Janusz Brzdek
Publisher : Academic Press
ISBN 13 : 0128098309
Total Pages : 238 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Ulam Stability of Operators by : Janusz Brzdek

Download or read book Ulam Stability of Operators written by Janusz Brzdek and published by Academic Press. This book was released on 2018-01-10 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ulam Stability of Operators presents a modern, unified, and systematic approach to the field. Focusing on the stability of functional equations across single variable, difference equations, differential equations, and integral equations, the book collects, compares, unifies, complements, generalizes, and updates key results. Whenever suitable, open problems are stated in corresponding areas. The book is of interest to researchers in operator theory, difference and functional equations and inequalities, differential and integral equations. Allows readers to establish expert knowledge without extensive study of other books Presents complex math in simple and clear language Compares, generalizes and complements key findings Provides numerous open problems

Stability of Mappings of Hyers-Ulam Type

Author : Themistocles M. Rassias
Publisher :
ISBN 13 :
Total Pages : 190 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Stability of Mappings of Hyers-Ulam Type by : Themistocles M. Rassias

Download or read book Stability of Mappings of Hyers-Ulam Type written by Themistocles M. Rassias and published by . This book was released on 1994 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Towards Ulam Type Multi Stability Analysis

Author : Safoura Rezaei Aderyani
Publisher : Springer Nature
ISBN 13 : 3031555643
Total Pages : 580 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Towards Ulam Type Multi Stability Analysis by : Safoura Rezaei Aderyani

Download or read book Towards Ulam Type Multi Stability Analysis written by Safoura Rezaei Aderyani and published by Springer Nature. This book was released on with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Towards Ulam Type Multi Stability Analysis

Author : Safoura Rezaei Aderyani
Publisher : Springer
ISBN 13 : 9783031555633
Total Pages : 0 pages
Book Rating : 4.5/5 (556 download)

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Book Synopsis Towards Ulam Type Multi Stability Analysis by : Safoura Rezaei Aderyani

Download or read book Towards Ulam Type Multi Stability Analysis written by Safoura Rezaei Aderyani and published by Springer. This book was released on 2024-05-13 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main target of this book is to present a new concept of Ulam-type stability, i.e., multi-stability, through the classical, well-known special functions and to obtain the best approximation error estimates by a different concept of perturbation stability including fuzzy approaches for uncertainty considerations. This stability allows us to obtain diverse approximations depending on various special functions that are initially chosen and to evaluate maximal stability and minimal error which enable us to obtain a unique optimal solution of functional equations, inequalities, and fractional equations. Stability analysis in the sense of the Ulam and its different kinds has received considerable attention from the researchers. However, how to effectively generalize the Ulam stability problems and to evaluate optimized controllability and stability are new issues. The multi-stability not only covers the previous concepts but also considers the optimization of the problem and provides a comprehensive discussion of optimizing the different types of the Ulam stabilities of mathematical models used in the natural sciences and engineering disciplines with fuzzy attitudes. Besides, this book also deals with nonlinear differential equations with various boundary conditions or initial value problems, based on the matrix Mittag-Leffler function, fixed point theory, as well as Babenko's approach to study uniqueness and existence of solutions. In general, the benefits for the readers can be concluded as follows: 1. Evaluates maximal stability with minimal error to get a unique optimal solution. 2. Discusses an optimal method of the alternative to study existence, uniqueness, and different types of Ulam stabilities under special consideration of the fuzzy approaches. 3. Delves into the new study of boundary value problems of fractional integro-differential equations with integral boundary conditions and variable coefficients.

Hyers-Ulam Stability of Ordinary Differential Equations

Author : Arun Kumar Tripathy
Publisher : CRC Press
ISBN 13 : 1000386902
Total Pages : 114 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Hyers-Ulam Stability of Ordinary Differential Equations by : Arun Kumar Tripathy

Download or read book Hyers-Ulam Stability of Ordinary Differential Equations written by Arun Kumar Tripathy and published by CRC Press. This book was released on 2021-05-24 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hyers-Ulam Stability of Ordinary Differential Equations undertakes an interdisciplinary, integrative overview of a kind of stability problem unlike the existing so called stability problem for Differential equations and Difference Equations. In 1940, S. M. Ulam posed the problem: When can we assert that approximate solution of a functional equation can be approximated by a solution of the corresponding equation before the audience at the University of Wisconsin which was first answered by D. H. Hyers on Banach space in 1941. Thereafter, T. Aoki, D. H. Bourgin and Th. M. Rassias improved the result of Hyers. After that many researchers have extended the Ulam's stability problems to other functional equations and generalized Hyer's result in various directions. Last three decades, this topic is very well known as Hyers-Ulam Stability or sometimes it is referred Hyers-Ulam-Rassias Stability. This book synthesizes interdisciplinary theory, definitions and examples of Ordinary Differential and Difference Equations dealing with stability problems. The purpose of this book is to display the new kind of stability problem to global audience and accessible to a broader interdisciplinary readership for e.g those are working in Mathematical Biology Modeling, bending beam problems of mechanical engineering also, some kind of models in population dynamics. This book may be a starting point for those associated in such research and covers the methods needed to explore the analysis. Features: The state-of-art is pure analysis with background functional analysis. A rich, unique synthesis of interdisciplinary findings and insights on resources. As we understand that the real world problem is heavily involved with Differential and Difference equations, the cited problems of this book may be useful in a greater sense as long as application point of view of this Hyers-Ulam Stability theory is concerned. Information presented in an accessible way for students, researchers, scientists and engineers.

Stability of Functional Equations of Ulam-Hyers-Rassias Type

Author : Stefan Czerwik
Publisher :
ISBN 13 : 9781574850574
Total Pages : 200 pages
Book Rating : 4.8/5 (55 download)

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Book Synopsis Stability of Functional Equations of Ulam-Hyers-Rassias Type by : Stefan Czerwik

Download or read book Stability of Functional Equations of Ulam-Hyers-Rassias Type written by Stefan Czerwik and published by . This book was released on 2003-07 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dynamic Equations on Time Scales

Author : Martin Bohner
Publisher : Springer Science & Business Media
ISBN 13 : 1461202019
Total Pages : 365 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Dynamic Equations on Time Scales by : Martin Bohner

Download or read book Dynamic Equations on Time Scales written by Martin Bohner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: On becoming familiar with difference equations and their close re lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Lecture Notes 312 (page 10), 1973] A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both. [E. T. BELL, Men of Mathematics, Simon and Schuster, New York (page 13/14), 1937] The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis [159] in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. This book is an intro duction to the study of dynamic equations on time scales. Many results concerning differential equations carryover quite easily to corresponding results for difference equations, while other results seem to be completely different in nature from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice, once for differential equa tions and once for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which is an arbitrary nonempty closed subset of the reals.

Stability of Functional Equations in Several Variables

Author : D.H. Hyers
Publisher : Springer Science & Business Media
ISBN 13 : 9780817640248
Total Pages : 330 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Stability of Functional Equations in Several Variables by : D.H. Hyers

Download or read book Stability of Functional Equations in Several Variables written by D.H. Hyers and published by Springer Science & Business Media. This book was released on 1998-09-01 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of stability of functional equations of several variables in the sense used here had its origins more than half a century ago when S. Ulam posed the fundamental problem and Donald H. Hyers gave the first significant partial solution in 1941. The subject has been revised and de veloped by an increasing number of mathematicians, particularly during the last two decades. Three survey articles have been written on the subject by D. H. Hyers (1983), D. H. Hyers and Th. M. Rassias (1992), and most recently by G. L. Forti (1995). None of these works included proofs of the results which were discussed. Furthermore, it should be mentioned that wider interest in this subject area has increased substantially over the last years, yet the pre sentation of research has been confined mainly to journal articles. The time seems ripe for a comprehensive introduction to this subject, which is the purpose of the present work. This book is the first to cover the classical results along with current research in the subject. An attempt has been made to present the material in an integrated and self-contained fashion. In addition to the main topic of the stability of certain functional equa tions, some other related problems are discussed, including the stability of the convex functional inequality and the stability of minimum points. A sad note. During the final stages of the manuscript our beloved co author and friend Professor Donald H. Hyers passed away.

Problems in Modern Mathematics

Author : Stanislaw M. Ulam
Publisher : Courier Corporation
ISBN 13 : 9780486495835
Total Pages : 182 pages
Book Rating : 4.4/5 (958 download)

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Book Synopsis Problems in Modern Mathematics by : Stanislaw M. Ulam

Download or read book Problems in Modern Mathematics written by Stanislaw M. Ulam and published by Courier Corporation. This book was released on 2004-06-23 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ulam, famous for his solution to the difficulties of initiating fusion in the hydrogen bomb, devised the well-known Monte-Carlo method. Here he presents challenges in the areas of set theory, algebra, metric and topological spaces, and topological groups. Issues in analysis, physical systems, and the use of computers as a heuristic aid are also addressed.

Dynamic Calculus and Equations on Time Scales

Author : Svetlin G. Georgiev
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111185192
Total Pages : 370 pages
Book Rating : 4.1/5 (111 download)

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Book Synopsis Dynamic Calculus and Equations on Time Scales by : Svetlin G. Georgiev

Download or read book Dynamic Calculus and Equations on Time Scales written by Svetlin G. Georgiev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-09-18 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computational Intelligence, Cyber Security and Computational Models. Models and Techniques for Intelligent Systems and Automation

Download Computational Intelligence, Cyber Security and Computational Models. Models and Techniques for Intelligent Systems and Automation PDF Online Free

Author : Geetha Ganapathi
Publisher : Springer
ISBN 13 : 9811307164
Total Pages : 262 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Computational Intelligence, Cyber Security and Computational Models. Models and Techniques for Intelligent Systems and Automation by : Geetha Ganapathi

Download or read book Computational Intelligence, Cyber Security and Computational Models. Models and Techniques for Intelligent Systems and Automation written by Geetha Ganapathi and published by Springer. This book was released on 2018-09-10 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the Third International Conference on Computational Intelligence, Cyber Security, and Computational Models, ICC3 2017, which was held in Coimbatore, India, in December 2017. The 15 papers presented in this volume were carefully reviewed and selected from 63 submissions. They were organized in topical sections named: computational intelligence; cyber security; and computational models.

Mathematics Without Boundaries

Author : Themistocles M. Rassias
Publisher : Springer
ISBN 13 : 1493911066
Total Pages : 783 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Mathematics Without Boundaries by : Themistocles M. Rassias

Download or read book Mathematics Without Boundaries written by Themistocles M. Rassias and published by Springer. This book was released on 2014-09-17 with total page 783 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the latest information.

Nonlinear Analysis and Variational Problems

Author : Panos M. Pardalos
Publisher : Springer Science & Business Media
ISBN 13 : 1441901582
Total Pages : 502 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Nonlinear Analysis and Variational Problems by : Panos M. Pardalos

Download or read book Nonlinear Analysis and Variational Problems written by Panos M. Pardalos and published by Springer Science & Business Media. This book was released on 2009-10-20 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization.

Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery

Author : Hongying Meng
Publisher : Springer Nature
ISBN 13 : 3030706656
Total Pages : 1925 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery by : Hongying Meng

Download or read book Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery written by Hongying Meng and published by Springer Nature. This book was released on 2021-06-26 with total page 1925 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of papers on the recent progresses in the state of the art in natural computation, fuzzy systems and knowledge discovery. The book is useful for researchers, including professors, graduate students, as well as R & D staff in the industry, with a general interest in natural computation, fuzzy systems and knowledge discovery. The work printed in this book was presented at the 2020 16th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD 2020), held in Xi'an, China, from 19 to 21 December 2020. All papers were rigorously peer-reviewed by experts in the areas.

Multiplicative Inverse Functional Equations

Author : B. V. Senthil Kumar
Publisher : Springer Nature
ISBN 13 : 3030453553
Total Pages : 124 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Multiplicative Inverse Functional Equations by : B. V. Senthil Kumar

Download or read book Multiplicative Inverse Functional Equations written by B. V. Senthil Kumar and published by Springer Nature. This book was released on 2020-04-06 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces readers to numerous multiplicative inverse functional equations and their stability results in various spaces. This type of functional equation can be of use in solving many physical problems and also has significant relevance in various scientific fields of research and study. In particular, multiplicative inverse functional equations have applications in electric circuit theory, physics, and relations connecting the harmonic mean and arithmetic mean of several values. Providing a wealth of essential insights and new concepts in the field of functional equations, the book is chiefly intended for researchers, graduate schools, graduate students, and educators, and can also used for seminars in analysis covering topics of functional equations.

Fractional Difference, Differential Equations, and Inclusions

Author : Saïd Abbas
Publisher : Elsevier
ISBN 13 : 044323602X
Total Pages : 400 pages
Book Rating : 4.4/5 (432 download)

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Book Synopsis Fractional Difference, Differential Equations, and Inclusions by : Saïd Abbas

Download or read book Fractional Difference, Differential Equations, and Inclusions written by Saïd Abbas and published by Elsevier. This book was released on 2024-01-16 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of fractional calculus (FC) is more than 300 years old, and it presumably stemmed from a question about a fractional-order derivative raised in communication between L'Hopital and Leibniz in the year 1695. This branch of mathematical analysis is regarded as the generalization of classical calculus, as it deals with the derivative and integral operators of fractional order. The tools of fractional calculus are found to be of great utility in improving the mathematical modeling of many natural phenomena and processes occurring in the areas of engineering, social, natural, and biomedical sciences. Fractional Difference, Differential Equations, and Inclusions: Analysis and Stability is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for several classes of functional fractional difference equations and inclusions. Some equations include delay effects of finite, infinite, or state-dependent nature. Others are subject to impulsive effect which may be fixed or non-instantaneous. The tools used to establish the existence results for the proposed problems include fixed point theorems, densifiability techniques, monotone iterative technique, notions of Ulam stability, attractivity and the measure of non-compactness as well as the measure of weak noncompactness. All the abstract results are illustrated by examples in applied mathematics, engineering, biomedical, and other applied sciences. Introduces notation, definitions, and foundational concepts of fractional q-calculus Presents existence and attractivity results for a class of implicit fractional q-difference equations in Banach and Fréchet spaces Focuses on the study of a class of coupled systems of Hilfer and Hilfer-Hadamard fractional differential equations