## Nonlinear Analysis: Approximation Theory, Optimization and ApplicationsMany 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 | |

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 |

### Other editions - View all

Nonlinear Analysis: Approximation Theory, Optimization and Applications Qamrul Hasan Ansari No preview available - 2016 |

Nonlinear Analysis: Approximation Theory, Optimization and Applications Qamrul Hasan Ansari No preview available - 2014 |

Nonlinear Analysis: Approximation Theory, Optimization and Applications Qamrul Hasan Ansari No preview available - 2014 |

### Common terms and phrases

allx Appl Banach space best approximation bounded closed convex subset codimension continuous contraction map convergent subsequence converges strongly convex function convex set deﬁned Deﬁnition denote dimensional dist(A equilibrium problems exists ﬁnite Fix(S ﬁxed point fixed point problems Fixed Point Theory following result G Fix(T G SX Hausdorff Hence hierarchical variational inequality Hilbert space HVIP hyperplane implies isotone projection cone iterative method L-Lipschitz Lemma llxn lower semicontinuous Math matrix measure of noncompactness metric projection metric space minimization problem minimizing sequence nonempty closed convex nonexpansive mappings nonlinear complementarity problem normed linear space optimization point theorem projection cone properties real Hilbert space reﬂexive satisﬁes semi-continuous sequence xn space H split feasibility problem Stieltjes matrix strictly convex strong convergence strongly monotone subspace Theorem topology uniformly convex variational inequality problem well-posed well-posedness xn+1