Nonlinear Functional Analysis

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.