Anita Tomar – författare

An applied understanding of functional analysis is essential for students pursuing research or careers in pure mathematics, applied mathematics, mathematical physics, and engineering, among other disciplines.Functional Analysis: Theory and Applications offers a comprehensive exploration of functional analysis. Authored by esteemed mathematicians with extensive expertise in the field, this book thoroughly introduces fundamental concepts in functional analysis, including Banach spaces, Hilbert spaces, operator theory, nonlinear analysis, linear operators, and normed spaces, and implements these in real-world problems across various scientific and engineering disciplines.The book's rigorous mathematical treatment is combined with worked examples, exercises and solutions, visual aids, application case studies, and future directions across all chapters to reinforce learning, while appendices offer supplementary materials, proofs of theorems, and tables of important results, among other resources.Offers a comprehensive introduction to functional analysis, essential for students pursuing research or careers in pure mathematics, applied mathematics, mathematical physics, and engineering, among other disciplinesFeatures worked examples, exercises and solutions, visual aids, application case studies, and future directions across all chapters to reinforce learningIntroduces and applies core frameworks in functional analysis, from Banach spaces to Hilbert spaces, operator theory, nonlinear analysis, linear operators, and normed spacesIncludes a solutions manual, PowerPoint lecture slides, a test bank, and supplementary reading list on supporting instructor and companion websites to aid learning and teaching

An applied understanding of functional analysis is essential for students pursuing research or careers in pure mathematics, applied mathematics, mathematical physics, and engineering, among other disciplines.Functional Analysis: Theory and Applications offers a comprehensive exploration of functional analysis. Authored by esteemed mathematicians with extensive expertise in the field, this book thoroughly introduces fundamental concepts in functional analysis, including Banach spaces, Hilbert spaces, operator theory, nonlinear analysis, linear operators, and normed spaces, and implements these in real-world problems across various scientific and engineering disciplines.The book's rigorous mathematical treatment is combined with worked examples, exercises and solutions, visual aids, application case studies, and future directions across all chapters to reinforce learning, while appendices offer supplementary materials, proofs of theorems, and tables of important results, among other resources. - Offers a comprehensive introduction to functional analysis, essential for students pursuing research or careers in pure mathematics, applied mathematics, mathematical physics, and engineering, among other disciplines- Features worked examples, exercises and solutions, visual aids, application case studies, and future directions across all chapters to reinforce learning- Introduces and applies core frameworks in functional analysis, from Banach spaces to Hilbert spaces, operator theory, nonlinear analysis, linear operators, and normed spaces- Includes a solutions manual, PowerPoint lecture slides, a test bank, and supplementary reading list on supporting instructor and companion websites to aid learning and teaching

Fixed-point theory initially emerged in the article demonstrating existence of solutions of differential equations, which appeared in the second quarter of the 18th century (Joseph Liouville, 1837). Later on, this technique was improved as a method of successive approximations (Charles Emile Picard, 1890) which was extracted and abstracted as a fixed-point theorem in the framework of complete normed space (Stefan Banach, 1922). It ensures presence as well as uniqueness of a fixed point, gives an approximate technique to really locate the fixed point and the a priori and a posteriori estimates for the rate of convergence. It is an essential device in the theory of metric spaces. Subsequently, it is stated that fixed-point theory is initiated by Stefan Banach. Fixed-point theorems give adequate conditions under which there exists a fixed point for a given function and enable us to ensure the existence of a solution of the original problem. In an extensive variety of scientific issues, beginning from different branches of mathematics, the existence of a solution is comparable to the existence of a fixed point for a suitable mapping. This book is an endeavour to present results in fixed point theory which are extensions, improvements and generalizations of classical and recent results in this area and touches on distinct research directions within the metric fixed-point theory. It provides new openings for further exploration and makes for an easily accessible source of knowledge. This book is apposite for young researchers who want to pursue their research in fixed-point theory and is the latest in the field, giving new techniques for the existence of a superior fixed point, a fixed point, a near fixed point, a fixed circle, a near fixed interval circle, a fixed disc, a near fixed interval disc, a coincidence point, a common fixed point, a coupled common fixed point, amiable fixed sets, strong coupled fixed points and so on, utilizing minimal conditions. It offers novel applications besides traditional applications which are applicable to real world problems. The book is self-contained and unified which will serve as a reference book to researchers who are in search of novel ideas. It will be a valued addition to the library.

This book explores cryptographic techniques by integrating Elliptic and Jacobian Elliptic Curve Cryptography with Ancient Indian Mathematics, optimizing security and computational efficiency. As digital security becomes vital, the rich mathematical heritage of ancient India offers profound insights into cryptography, bridging historical wisdom with cutting-edge security solutions.Key frameworks- algebra, analysis, and optimization- enhance point operations like addition and doubling in cryptographic protocols. The book explores trilinear pairing and cryptographic schemes over specialized rings, leveraging projective geometry and algebraic structures to enhance encryption and decryption methods. Covering foundational concepts, algorithms, and applications, the book highlights how ancient Indian insights can improve Elliptic Curve Cryptography, Jacobian Elliptic Curve Cryptography, and trilinear pairing.Applications span secure vehicular communication using fog computing, blockchain-based authentication, and cloud security. It is targeted at cryptographers, mathematicians, and computer scientists and provides algorithmic innovations, security proofs, structured exercises, and real-world case studies.

This contributed volume contains chapters on various fixed-point theorems, including those in metric, b-metric and partial metric spaces. The book addresses the need for rigorous analytical methods in optimization, computational mathematics and applied sciences. By offering innovative solutions through iterative schemes and contraction principles, it bridges the gap between abstract mathematical principles and practical problem-solving approaches. The concept of fixed points has deep mathematical significance, influencing both theoretical frameworks and real-world applications. The book highlights the applications of fixed-point theory, presenting fundamental concepts and modern advancements, in diverse fields such as traffic control systems, stock market analysis, iterative algorithms and differential equations.

This contributed volume contains chapters on various fixed-point theorems, including those in metric, b-metric and partial metric spaces. The book addresses the need for rigorous analytical methods in optimization, computational mathematics and applied sciences. By offering innovative solutions through iterative schemes and contraction principles, it bridges the gap between abstract mathematical principles and practical problem-solving approaches. The concept of fixed points has deep mathematical significance, influencing both theoretical frameworks and real-world applications. The book highlights the applications of fixed-point theory, presenting fundamental concepts and modern advancements, in diverse fields such as traffic control systems, stock market analysis, iterative algorithms and differential equations.

This book offers a comprehensive exploration of the Banach contraction principle and its many facets. A compilation of chapters authored by global experts, it is aimed at researchers and graduate students in mathematics. The content covers the Banach contraction principle, its generalizations, extensions, consequences and applications, focusing on both single-valued and multi-valued mappings across various spaces. While discussing theoretical foundations, this book uniquely emphasizes the practical applications of the Banach contraction principle in real-world problem-solving scenarios.Each chapter addresses specific topics, including fractals, fractional differentials, integral equations, elastic beam problems and mathematical modeling and analysis of electrical circuits. These diverse subjects showcase the principle’s versatility in solving complex issues that go beyond theoretical mathematics. By highlighting Banach’s contraction principle as a lasting legacy, the book not only honours past mathematical achievements but also anticipates future innovations in industrial and applied mathematics. It underscores the enduring relevance of the principle, ensuring its continued prominence in mathematical discourse and its pivotal role in driving advancements across the field. This comprehensive exploration catalyzes inspiring future developments in mathematical research.