Towards Ulam Type Multi Stability Analysis
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Towards Ulam Type Multi Stability Analysis
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Author : Safoura Rezaei Aderyani
language : en
Publisher: Springer Nature
Release Date : 2024-04-29
Towards Ulam Type Multi Stability Analysis written by Safoura Rezaei Aderyani and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-29 with Computers categories.
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.
Towards Ulam Type Multi Stability Analysis
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Author : Safoura Rezaei Aderyani
language : en
Publisher: Springer
Release Date : 2024-05-13
Towards Ulam Type Multi Stability Analysis written by Safoura Rezaei Aderyani and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-13 with Technology & Engineering categories.
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.
Frontiers In Functional Equations And Analytic Inequalities
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Author : George A. Anastassiou
language : en
Publisher: Springer Nature
Release Date : 2019-11-23
Frontiers In Functional Equations And Analytic Inequalities written by George A. Anastassiou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-23 with Mathematics categories.
This volume presents cutting edge research from the frontiers of functional equations and analytic inequalities active fields. It covers the subject of functional equations in a broad sense, including but not limited to the following topics: Hyperstability of a linear functional equation on restricted domains Hyers–Ulam’s stability results to a three point boundary value problem of nonlinear fractional order differential equations Topological degree theory and Ulam’s stability analysis of a boundary value problem of fractional differential equations General Solution and Hyers-Ulam Stability of Duo Trigintic Functional Equation in Multi-Banach Spaces Stabilities of Functional Equations via Fixed Point Technique Measure zero stability problem for the Drygas functional equation with complex involution Fourier Transforms and Ulam Stabilities of Linear Differential Equations Hyers–Ulam stability of a discrete diamond–alpha derivative equation Approximate solutions of an interesting new mixed type additive-quadratic-quartic functional equation. The diverse selection of inequalities covered includes Opial, Hilbert-Pachpatte, Ostrowski, comparison of means, Poincare, Sobolev, Landau, Polya-Ostrowski, Hardy, Hermite-Hadamard, Levinson, and complex Korovkin type. The inequalities are also in the environments of Fractional Calculus and Conformable Fractional Calculus. Applications from this book's results can be found in many areas of pure and applied mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such, this volume is suitable for researchers, graduate students and related seminars, and all science and engineering libraries. The exhibited thirty six chapters are self-contained and can be read independently and interesting advanced seminars can be given out of this book.
Functional Equations And Inequalities Solutions And Stability Results
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Author : John Michael Rassias
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017-03-20
Functional Equations And Inequalities Solutions And Stability Results written by John Michael Rassias 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 2017-03-20 with Mathematics categories.
This volume covers the topic in functional equations in a broad sense and is written by authors who are in this field for the past 50 years. It contains the basic notions of functional equations, the methods of solving functional equations, the growth of functional equations in the last four decades and an extensive reference list on fundamental research papers that investigate the stability results of different types of functional equations and functional inequalities. This volume starts by taking the reader from the fundamental ideas to higher levels of results that appear in recent research papers. Its step-by-step expositions are easy for the reader to understand and admire the elegant results and findings on the stability of functional equations.
Ulam Type Stability
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Author : Janusz Brzdęk
language : en
Publisher: Springer Nature
Release Date : 2019-10-29
Ulam Type Stability written by Janusz Brzdęk and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-29 with Mathematics categories.
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.
Fractional Differential Equations Inclusions And Inequalities With Applications
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Author : Sotiris K. Ntouyas
language : en
Publisher: MDPI
Release Date : 2020-11-09
Fractional Differential Equations Inclusions And Inequalities With Applications written by Sotiris K. Ntouyas and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-09 with Mathematics categories.
During the last decade, there has been an increased interest in fractional differential equations, inclusions, and inequalities, as they play a fundamental role in the modeling of numerous phenomena, in particular, in physics, biomathematics, blood flow phenomena, ecology, environmental issues, viscoelasticity, aerodynamics, electrodynamics of complex medium, electrical circuits, electron-analytical chemistry, control theory, etc. This book presents collective works published in the recent Special Issue (SI) entitled "Fractional Differential Equation, Inclusions and Inequalities with Applications" of the journal Mathematics. This Special Issue presents recent developments in the theory of fractional differential equations and inequalities. Topics include but are not limited to the existence and uniqueness results for boundary value problems for different types of fractional differential equations, a variety of fractional inequalities, impulsive fractional differential equations, and applications in sciences and engineering.
Mathematics Without Boundaries
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Author : Themistocles M. Rassias
language : en
Publisher: Springer
Release Date : 2014-09-17
Mathematics Without Boundaries 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 2014-09-17 with Mathematics categories.
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.
Mathematical Analysis And Applications
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Author : Michael Ruzhansky
language : en
Publisher: John Wiley & Sons
Release Date : 2018-05-11
Mathematical Analysis And Applications written by Michael Ruzhansky and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-11 with Mathematics categories.
An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.
Nonlinear Analysis
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Author : Panos M. Pardalos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-02
Nonlinear Analysis written by Panos M. Pardalos 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 2012-06-02 with Mathematics categories.
The volume will consist of about 40 articles written by some very influential mathematicians of our time and will expose the latest achievements in the broad area of nonlinear analysis and its various interdisciplinary applications.
Functional Equations In Mathematical Analysis
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Author : Themistocles M. Rassias
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-18
Functional Equations In Mathematical Analysis written by Themistocles M. Rassias 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 2011-09-18 with Mathematics categories.
The stability problem for approximate homomorphisms, or the Ulam stability problem, was posed by S. M. Ulam in the year 1941. The solution of this problem for various classes of equations is an expanding area of research. In particular, the pursuit of solutions to the Hyers-Ulam and Hyers-Ulam-Rassias stability problems for sets of functional equations and ineqalities has led to an outpouring of recent research. This volume, dedicated to S. M. Ulam, presents the most recent results on the solution to Ulam stability problems for various classes of functional equations and inequalities. Comprised of invited contributions from notable researchers and experts, this volume presents several important types of functional equations and inequalities and their applications to problems in mathematical analysis, geometry, physics and applied mathematics. "Functional Equations in Mathematical Analysis" is intended for researchers and students in mathematics, physics, and other computational and applied sciences.