Nonlinear Analysis: Approximation Theory, Optimization and Applications

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Qamrul Hasan Ansari
Springer, Jun 5, 2014 - Mathematics - 352 pages
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.
 

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Contents

1 Best Proximity Points
1
2 Semicontinuity Properties of Metric Projections
33
3 Convergence of Slices Geometric Aspects in Banach Spaces and Proximinality
60
4 Measures of Noncompactness and WellPosed Minimization Problems
109
5 WellPosedness Regularization and Viscosity Solutions of Minimization Problems
135
6 Best Approximation in Nonlinear Functional Analysis
165
7 Hierarchical Minimization Problems and Applications
199
8 Triple Hierarchical Variational Inequalities
230
9 Split Feasibility and Fixed Point Problems
281
10 Isotone Projection Cones and Nonlinear Complementarity Problems
323
Index
349
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About the author (2014)

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.

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