Manisha Aggarwal – författare
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3 produkter
3 produkter
975 kr
Skickas inom 3-6 vardagar
The monograph targets a huge variety of characterizations of cofinally complete metric spaces. These spaces are studied in terms of several properties of some classes of functions between metric spaces that are stronger than the continuous functions such as Cauchy-regular, uniformly continuous, strongly uniformly continuous, and various Lipschitz-type functions. There is one chapter that is dedicated to studying cofinally complete metric spaces in terms of hyperspace and function space topologies. Along with that, various characterizations are studied in terms of geometric functionals, sequences, Cantor-type conditions, etc. The study of such spaces is interesting as well as it has nice connections with various other branches of mathematics such as convex analysis, optimization theory, fixed point theory, functional analysis and approximation theory. But until now, there has been no textbook or research monograph which presents the entire theory of these spaces in a comprehensive way. The study of the aforesaid spaces and their variants is still a vibrant area of research, and many prominent researchers are working in this area.The book is targeted at researchers as well as graduate students interested in real functions, analysis on metric spaces, topology, and the aforementioned. Since the monograph often discusses various properties of Lipschitz-type functions, it would be of interest to people interested in PDEs as well.
1 180 kr
Skickas inom 3-6 vardagar
This book offers the comprehensive study of one of the foundational topics in Mathematics, known as Metric Spaces. The book delivers the concepts in an appropriate and concise manner, at the same time rich in illustrations and exercise problems. Special focus has been laid on important theorems like Baire's Category theorem, Heine-Borel theorem, Ascoli-Arzela Theorem, etc, which play a crucial role in the study of metric spaces.The additional chapter on Cofinal completeness, UC spaces and finite chainability makes the text unique of its kind. This helps the students in: Readers will also find brief discussions on various subtleties of continuity like subcontinuity, upper semi-continuity, lower semi-continuity, etc. The interested readers will be motivated to explore the special classes of functions between metric spaces to further extent.Consequently, the book becomes a complete package: it makes the foundational pillars strong and develops the interest of students to pursue research in metric spaces. The book is useful for third and fourth year undergraduate students and it is also helpful for graduate students and researchers.
1 837 kr
Kommande
This book is designed as a two-semester text. The first semester is devoted to Banach and Hilbert spaces, while the second semester focuses on operator theory.The book aims not only to present the core concepts in a clear and concise manner, but also to enrich the reader's understanding through numerous illustrations and a wide range of exercise problems. Special focus has been laid on important theorems like open map theorem, closed graph theorem, Hahn-Banach theorems, principle of uniform boundedness, etc, which play a crucial role in the study of functional analysis. Moreover, the reader will also find brief discussions on various tricky topics like comparison between two types of adjoint operators — Hilbert space adjoint and Banach space adjoint, etc. Careful attention has been paid on the hypothesis of the results and counterexamples have been provided for their significance.The prerequisites for this book include undergraduate courses in real analysis, linear algebra and basic point set topology (for example, metric spaces). Beyond this, some familiarity with measure theory and Lebesgue integration is desirable, but not essential. Most of the use of measure theory and Lebesgue integration occurs in limited ways.