Böcker av Ravi P. Agarwal

This book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics. The authors begin with an overview of the extension of metric spaces. Readers are introduced to general fixed-point theorems while comparing and contrasting important and insignificant metric spaces. The book is intended to be self-contained and serves as a unique resource for researchers in various disciplines.

This monograph is devoted to developing a theory of combined measure and shift invariance of time scales with the related applications to shift functions and dynamic equations. The study of shift closeness of time scales is significant to investigate the shift functions such as the periodic functions, the almost periodic functions, the almost automorphic functions, and their generalizations with many relevant applications in dynamic equations on arbitrary time scales.First proposed by S. Hilger, the time scale theory-a unified view of continuous and discrete analysis-has been widely used to study various classes of dynamic equations and models in real-world applications. Measure theory based on time scales, in its turn, is of great power in analyzing functions on time scales or hybrid domains. As a new and exciting type of mathematics-and more comprehensive and versatile than the traditional theories of differential and difference equations-, the time scale theory can precisely depict the continuous-discrete hybrid processes and is an optimal way forward for accurate mathematical modeling in applied sciences such as physics, chemical technology, population dynamics, biotechnology, and economics and social sciences.Graduate students and researchers specializing in general dynamic equations on time scales can benefit from this work, fostering interest and further research in the field. It can also serve as reference material for undergraduates interested in dynamic equations on time scales. Prerequisites include familiarity with functional analysis, measure theory, and ordinary differential equations.

This book systematically establishes the almost periodic theory of dynamic equations and presents applications on time scales in fuzzy mathematics and uncertainty theory. The authors introduce a new division of fuzzy vectors depending on a determinant algorithm and develop a theory of almost periodic fuzzy multidimensional dynamic systems on time scales. Several applications are studied; in particular, a new type of fuzzy dynamic systems called fuzzy q-dynamic systems (i.e. fuzzy quantum dynamic systems) is presented. The results are not only effective on classical fuzzy dynamic systems, including their continuous and discrete situations, but are also valid for other fuzzy multidimensional dynamic systems on various hybrid domains. In an effort to achieve more accurate analysis in real world applications, the authors propose a number of uncertain factors in the theory. As such, fuzzy dynamical models, interval-valued functions, differential equations, fuzzy-valued differential equations, and their applications to dynamic equations on time scales are considered.

Preface.- Lyapunov-Type Inequalities for Second-Order Linear Differential Equations.- Lyapunov-Type Inequalities for Higher-Order Linear Differential Equations.- Lyapunov-Type Inequalities for Half-Linear Differential Equations.- Lyapunov-Type Inequalities for Nonlinear Differential Systems.- Lyapunov-Type Inequalities for Fractional Differential Equations.- Lyapunov-Type Inequalities for Partial Differential Equations.- Lyapunov-Type Inequalities for Difference Equations.- Lyapunov-Type Inequalities for Dynamic Equations on Time Scales.- References.- Index.

While many problems can be solved at the undergraduate level, a number of challenging real-life applications have also been included as a way to motivate further research in this vast and fascinating field.

Devoted to dynamic inequalities of Hardy type and extensions and generalizations via convexity on a time scale T, this book gives the time scale versions of a wide range of inequalities, following their histories and development. Each section in self-contained and one can see the relationship between the time scale versions.

Researchers in the fields of mathematical modeling, mathematical biology, and population dynamics will be particularly interested in this material.

This book offers advanced graduates and researchers a trove of key results in the study of convergence, in both real and complex domains. It explores new and more efficient applications developed by the authors for studies of optimization and analysis.

Interest in the mathematical analysis of multifunctions has increased rapidly. This volume encompasses the mathematical analysis of multifunctions and contains 29 research articles from leading mathematicians in this area.

This work introduces readers to the topic of maximal regularity for difference equations. This book is intended for graduate students and researchers in the area of difference equations, particularly those with advance knowledge of and interest in functional analysis.

This book provides a compact, but thorough, introduction to the subject of Real Analysis. It is intended for a senior undergraduate and for a beginning graduate one-semester course.

A study of difference equations and inequalities. It offers real-world examples and uses of difference equations in probability theory, queuing and statistical problems, stochastic time series, combinatorial analysis, number theory, geometry, electrical networks, quanta in radiation, genetics, economics, psychology, and sociology.

Summarizes the qualitative theory of differential equations with or without delays, collecting oscillation studies important to applications and further developments in mathematics, physics, engineering, and biology. This work explores key aspects of the oscillation of dynamic equations on time scales.