Nonlinear Analysis

Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.

Presents a thorough and coherent introduction to some core topics from nonlinear analysis, namely, approximation theory, optimization theory, theory of variational inequalities and fixed point theory Discusses the concept that forms the basis of current approximation methods, variational inequalities, optimization and fixed point theory Focuses on applications of nonlinear analysis, approximation theory and optimization Includes supplementary material: sn.pub/extras

Autorentext

QAMRUL HASAN ANSARI is professor at the Department of Mathematics, Aligarh Muslim University, Aligarh, India. He has been visiting professor at several universities, namely, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia; National Sun Yat-sen University, Kaohsiung, Taiwan. He has visited several universities across the globe to deliver his talks. His main areas of research are variational analysis, optimization, convex analysis and fixed-point theory. He has published more than 150 research papers in international journals. He is the author of two books, and editor of three contributed volumes. He is the associate editor of Journal of Optimization Theory and Applications and Fixed Point Theory and Applications. He has also served as associate editor or lead guest editor of several journals, namely, Journal of Inequalities and Applications, Journal of Global Optimization, Positivity, Applicable Analysis.

Inhalt
Chapter 1. Best Proximity Points.- Chapter 2. Semi-Continuity Properties of Metric Projections.- Chapter 3. Convergence of Slices, Geometric Aspects in Banach Spaces and Proximinality.- Chapter 4. Measures of Non compactness and Well-Posed Minimization Problems.- Chapter 5. Well-Posedness, Regularization and Viscosity Solutions of Minimization Problems.- Chapter 6. Best Approximation in Nonlinear Functional Analysis.- Chapter 7. Hierarchical Minimization Problems and Applications.- Chapter 8. Triple Hierarchical Variational Inequalities.- Chapter 9. Split Feasibility and Fixed Point Problems.- Chapter 10. Isotone Projection Cones and Nonlinear Complementarity Problems.