Subject Code: MA7L020 Subject Name:  Nonlinear Functional Analysis L-T-P: 3-1-0 Credit:4
Pre-requisite(s):  Functional Analysis (MA5L011)
Fixed point theory, Banach contraction mapping theorem, contractive type mappings, generalization of Banach contraction mapping theorem, fixed point theorem of other types. Nonlinear operators, monotone, strictly monotone and strongly monotone operators, their properties and applications. Variational inequalities and complementarity problem. Approximation theory, theory of best approximation and farthest points. Calculus of Banach Space, Frechet and Gateaux differentiability, strict convexity and uniform convexity of norms, semi inner product space.
Text Books:
  1. Zeidler E. Nonlinear Functional Analysis and its applications, Springer
  2. Ambrosetti A., Arcoya D., Birkhauser. An Introduction to Nonlinear Functional Analysis and Elleptic Problems,
References Books:
  1. Debnath L. and Mikusinski P., Hilbert Spaces with Applications, Academic Press
  2. Kinderleherer D., Stampacchia G. An Introduction to Variational Inequalities and their Applications, Academic Press
  3. Tinsley Oden  J., Demkowicz L. Applied Functional Analysis, CRC Press