Download or read book Summability Theory and Its Applications written by Feyzi Başar and published by CRC Press. This book was released on 2022-06-27 with total page 865 pages. Available in PDF, EPUB and Kindle. Book excerpt: Summability Theory and Its Applications explains various aspects of summability and demonstrates its applications in a rigorous and coherent manner. The content can readily serve as a reference or as a useful series of lecture notes on the subject. This substantially revised new edition includes brand new material across several chapters as well as several corrections, including: the addition of the domain of Cesaro matrix C(m) of order m in the classical sequence spaces to Chapter 4; and introducing the domain of four-dimensional binomial matrix in the spaces of bounded, convergent in the Pringsheim's sense, both convergent in the Pringsheim's sense and bounded, and regularly convergent double sequences, in Chapter 7. Features Investigates different types of summable spaces and computes their dual Suitable for graduate students and researchers with a (special) interest in spaces of single and double sequences, matrix transformations and domains of triangle matrices Can serve as a reference or as supplementary reading in a computational physics course, or as a key text for special Analysis seminars.
Download or read book Summability Theory and Its Applications written by Feyzi Başar and published by CRC Press. This book was released on 2022-06-27 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: Summability Theory and Its Applications explains various aspects of summability and demonstrates its applications in a rigorous and coherent manner. The content can readily serve as a reference or as a useful series of lecture notes on the subject. This substantially revised new edition includes brand new material across several chapters as well as several corrections, including: the addition of the domain of Cesaro matrix C(m) of order m in the classical sequence spaces to Chapter 4; and introducing the domain of four-dimensional binomial matrix in the spaces of bounded, convergent in the Pringsheim's sense, both convergent in the Pringsheim's sense and bounded, and regularly convergent double sequences, in Chapter 7. Features Investigates different types of summable spaces and computes their dual Suitable for graduate students and researchers with a (special) interest in spaces of single and double sequences, matrix transformations and domains of triangle matrices Can serve as a reference or as supplementary reading in a computational physics course, or as a key text for special Analysis seminars.
Download or read book Classical and Modern Methods in Summability written by Johann Boos and published by Clarendon Press. This book was released on 2000 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Summability is a mathematical topic with a long tradition and many applications in, for example, function theory, number theory, and stochastics. It was originally based on classical analytical methods, but was strongly influenced by modern functional analytical methods during the last seven decades. The present book aims to introduce the reader to the wide field of summability and its applications, and provides an overview of the most important classical and modern methods used. Part I contains a short general introduction to summability, the basic classical theory concerning mainly inclusion theorems and theorems of the Silverman-Toeplitz type, a presentation of the most important classes of summability methods, Tauberian theorems, and applications of matrix methods. The proofs in Part I are exclusively done by applying classical analytical methods. Part II is concerned with modern functional analytical methods in summability, and contains the essential functional analytical basis required in later parts of the book, topologization of sequence spaces as K- and KF-spaces, domains of matrix methods as FK-spaces and their topological structure. In this part the proofs are of functional analytical nature only. Part III of the present book deals with topics in summability and topological sequence spaces which require the combination of classical and modern methods. It covers investigations of the constistency of matrix methods and of the bounded domain of matrix methods via Saks space theory, and the presentation of some aspects in topological sequence spaces. Lecturers, graduate students, and researchers working in summability and related topics will find this book a useful introduction and reference work.
Download or read book Functional Analysis and Summability written by P.N. Natarajan and published by CRC Press. This book was released on 2020-09-08 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are excellent books on both functional analysis and summability. Most of them are very terse. In Functional Analysis and Summability, the author makes a sincere attempt for a gentle introduction of these topics to students. In the functional analysis component of the book, the Hahn–Banach theorem, Banach–Steinhaus theorem (or uniform boundedness principle), the open mapping theorem, the closed graph theorem, and the Riesz representation theorem are highlighted. In the summability component of the book, the Silverman–Toeplitz theorem, Schur’s theorem, the Steinhaus theorem, and the Steinhaus-type theorems are proved. The utility of functional analytic tools like the uniform boundedness principle to prove some results in summability theory is also pointed out. Features A gentle introduction of the topics to the students is attempted. Basic results of functional analysis and summability theory and their applications are highlighted. Many examples are provided in the text. Each chapter ends with useful exercises. This book will be useful to postgraduate students, pre-research level students, and research scholars in mathematics. Students of physics and engineering will also find this book useful since topics in the book also have applications in related areas.
Download or read book Current Topics in Summability Theory and Applications written by Hemen Dutta and published by Springer. This book was released on 2016-04-28 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses recent developments in and contemporary research on summability theory, including general summability methods, direct theorems on summability, absolute and strong summability, special methods of summability, functional analytic methods in summability, and related topics and applications. All contributing authors are eminent scientists, researchers and scholars in their respective fields, and hail from around the world. The book can be used as a textbook for graduate and senior undergraduate students, and as a valuable reference guide for researchers and practitioners in the fields of summability theory and functional analysis. Summability theory is generally used in analysis and applied mathematics. It plays an important part in the engineering sciences, and various aspects of the theory have long since been studied by researchers all over the world.
Download or read book An Introductory Course in Summability Theory written by Ants Aasma and published by John Wiley & Sons. This book was released on 2017-04-03 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory course in summability theory for students, researchers, physicists, and engineers In creating this book, the authors’ intent was to provide graduate students, researchers, physicists, and engineers with a reasonable introduction to summability theory. Over the course of nine chapters, the authors cover all of the fundamental concepts and equations informing summability theory and its applications, as well as some of its lesser known aspects. Following a brief introduction to the history of summability theory, general matrix methods are introduced, and the Silverman-Toeplitz theorem on regular matrices is discussed. A variety of special summability methods, including the Nörlund method, the Weighted Mean method, the Abel method, and the (C, 1) - method are next examined. An entire chapter is devoted to a discussion of some elementary Tauberian theorems involving certain summability methods. Following this are chapters devoted to matrix transforms of summability and absolute summability domains of reversible and normal methods; the notion of a perfect matrix method; matrix transforms of summability and absolute summability domains of the Cesàro and Riesz methods; convergence and the boundedness of sequences with speed; and convergence, boundedness, and summability with speed. • Discusses results on matrix transforms of several matrix methods • The only English-language textbook describing the notions of convergence, boundedness, and summability with speed, as well as their applications in approximation theory • Compares the approximation orders of Fourier expansions in Banach spaces by different matrix methods • Matrix transforms of summability domains of regular perfect matrix methods are examined • Each chapter contains several solved examples and end-of-chapter exercises, including hints for solutions An Introductory Course in Summability Theory is the ideal first text in summability theory for graduate students, especially those having a good grasp of real and complex analysis. It is also a valuable reference for mathematics researchers and for physicists and engineers who work with Fourier series, Fourier transforms, or analytic continuation. ANTS AASMA, PhD, is Associate Professor of Mathematical Economics in the Department of Economics and Finance at Tallinn University of Technology, Estonia. HEMEN DUTTA, PhD, is Senior Assistant Professor of Mathematics at Gauhati University, India. P.N. NATARAJAN, PhD, is Formerly Professor and Head of the Department of Mathematics, Ramakrishna Mission Vivekananda College, Chennai, Tamilnadu, India.
Download or read book Asymptotics and Borel Summability written by Ovidiu Costin and published by CRC Press. This book was released on 2008-12-04 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, tr
Download or read book Soft Computing Techniques and Applications in Mechanical Engineering written by Ram, Mangey and published by IGI Global. This book was released on 2017-12-29 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: The evolution of soft computing applications has offered a multitude of methodologies and techniques that are useful in facilitating new ways to address practical and real scenarios in a variety of fields. In particular, these concepts have created significant developments in the engineering field. Soft Computing Techniques and Applications in Mechanical Engineering is a pivotal reference source for the latest research findings on a comprehensive range of soft computing techniques applied in various fields of mechanical engineering. Featuring extensive coverage on relevant areas such as thermodynamics, fuzzy computing, and computational intelligence, this publication is an ideal resource for students, engineers, research scientists, and academicians involved in soft computing techniques and applications in mechanical engineering areas.
Download or read book Summability Theory and Its Applications written by Robert Ellis Powell and published by . This book was released on 1972 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integral Transformations Operational Calculus and Their Applications written by Hari Mohan Srivastava and published by MDPI. This book was released on 2021-01-20 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of a collection of 14 accepted submissions (including several invited feature articles) to the Special Issue of MDPI's journal Symmetry on the general subject area of integral transformations, operational calculus and their applications from many different parts around the world. The main objective of the Special Issue was to gather review, expository, and original research articles dealing with the state-of-the-art advances in integral transformations and operational calculus as well as their multidisciplinary applications, together with some relevance to the aspect of symmetry. Various families of fractional-order integrals and derivatives have been found to be remarkably important and fruitful, mainly due to their demonstrated applications in numerous diverse and widespread areas of mathematical, physical, chemical, engineering, and statistical sciences. Many of these fractional-order operators provide potentially useful tools for solving ordinary and partial differential equations, as well as integral, differintegral, and integro-differential equations; fractional-calculus analogues and extensions of each of these equations; and various other problems involving special functions of mathematical physics and applied mathematics, as well as their extensions and generalizations in one or more variables.
Download or read book Current Trends in Mathematical Analysis and Its Interdisciplinary Applications written by Hemen Dutta and published by Springer Nature. This book was released on 2019-08-23 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research. Each of the 23 carefully reviewed chapters was written by experienced expert(s) in respective field, and will enrich readers’ understanding of the respective research problems, providing them with sufficient background to understand the theories, methods and applications discussed. The book’s main goal is to highlight the latest trends and advances, equipping interested readers to pursue further research of their own. Given its scope, the book will especially benefit graduate and PhD students, researchers in the applied sciences, educators, and engineers with an interest in recent developments in the interdisciplinary applications of mathematical analysis.
Download or read book Sequence Spaces written by Mohammad Mursaleen and published by CRC Press. This book was released on 2020-03-10 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at both experts and non-experts with an interest in getting acquainted with sequence spaces, matrix transformations and their applications. It consists of several new results which are part of the recent research on these topics. It provides different points of view in one volume, e.g. their topological properties, geometry and summability, fuzzy valued study and more. This book presents the important role sequences and series play in everyday life, it covers geometry of Banach Sequence Spaces, it discusses the importance of generalized limit, it offers spectrum and fine spectrum of several linear operators and includes fuzzy valued sequences which exhibits the study of sequence spaces in fuzzy settings. This book is the main attraction for those who work in Sequence Spaces, Summability Theory and would also serve as a good source of reference for those involved with any topic of Real or Functional Analysis.
Download or read book Advances in Applied Mathematical Analysis and Applications written by Mangey Ram and published by CRC Press. This book was released on 2022-09-01 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, applied mathematics has been used in all novel disciplines of scientific development. Advances in Applied Mathematical Problems summarizes interdisciplinary work within the field of applied mathematics. The topics discussed in the book include:• Similarity Solutions of Spherical Shock Waves in a Self-Gravitating Ideal Gas• Dual Solutions for Finite Element Analysis of Unsteady Hydromagnetic Stagnation Point Flow of Water Nanofluid Generated by Stretching Sheet• Multiparametric modeling of carbon cycle in temperate wetlands for regional climate change analysis using satellite data• An Intelligent Neuro Fuzzy System for Pattern Classification• Fuzzy inventory model with demand, deterioration and inflation: a comparative study through NGTFN and CNTFN• Summability and its application for the stability of the system• Design Of Manufacturing, Control, And Automation Systems• SEIR - Application for Crop through Water and Soil Texture• Advances in radial basis functions• Modeling For Time Period Of Natural Frequency For Non-Homogeneous Square Plate With Variable Thickness And Temperature Effect• A Study On Metric Fixed Point Theorems Satisfying Integral Type Contractions • Objective Function – In Radiometric Studies –Application to Agrs Surveys Associated With Radon• Modelling Kernel Function in Black body Radiation Inversion
Download or read book Studies on Divergent Series and Summability and The Asymptotic Developments of Functions Defined by Maclaurin Series written by Walter B. Ford and published by American Mathematical Soc.. This book was released on 1960-01-30 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers 2 main topics: asymptotic series and the theory of summability. This book provides a discussion of nowhere convergent asymptotic series that includes the so-called MacLaurent summation formula, determining asymptotic expansions of various classes of functions, and the study of asymptotic solutions of linear ordinary differential equations.
Download or read book APPLICATIONS OF STATISTICS ARTIFICIAL INTELLIGENCE IN EMERGING SCENARIOS 2023 written by Prof. Monalisha Pattnaik and published by Archers & Elevators Publishing House. This book was released on with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Divergent Series Summability and Resurgence I written by Claude Mitschi and published by Springer. This book was released on 2016-08-27 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential equations, their formal solutions at singular points, their monodromy and their differential Galois groups. The Riemann-Hilbert problem is discussed from Bolibrukh’s point of view. The second part expounds 1-summability and Ecalle’s theory of resurgence under fairly general conditions. It contains numerous examples and presents an analysis of the singularities in the Borel plane via “alien calculus”, which provides a full description of the Stokes phenomenon for linear or non-linear differential or difference equations. The first of a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists interested in geometric, algebraic or local analytic properties of dynamical systems. It includes useful exercises with solutions. The prerequisites are a working knowledge of elementary complex analysis and differential algebra.
Download or read book Lebesgue Points and Summability of Higher Dimensional Fourier Series written by Ferenc Weisz and published by Springer Nature. This book was released on 2021-06-12 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the summability of higher dimensional Fourier series, and generalizes the concept of Lebesgue points. Focusing on Fejér and Cesàro summability, as well as theta-summation, readers will become more familiar with a wide variety of summability methods. Within the theory of higher dimensional summability of Fourier series, the book also provides a much-needed simple proof of Lebesgue’s theorem, filling a gap in the literature. Recent results and real-world applications are highlighted as well, making this a timely resource. The book is structured into four chapters, prioritizing clarity throughout. Chapter One covers basic results from the one-dimensional Fourier series, and offers a clear proof of the Lebesgue theorem. In Chapter Two, convergence and boundedness results for the lq-summability are presented. The restricted and unrestricted rectangular summability are provided in Chapter Three, as well as the sufficient and necessary condition for the norm convergence of the rectangular theta-means. Chapter Four then introduces six types of Lebesgue points for higher dimensional functions. Lebesgue Points and Summability of Higher Dimensional Fourier Series will appeal to researchers working in mathematical analysis, particularly those interested in Fourier and harmonic analysis. Researchers in applied fields will also find this useful.
