Nonlinear Analysis : Approximation Theory Optimization and Applications 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 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