Some Topics in Fixed Point Theory: Non Linear Functional Analysis

Due to computer aided numerical analysis, approximating fixed point and convergence of iterative sequence have achieved importance. The study of random fixed points has been an active area of contemporary research in mathematics. Due to frequent confrontation with problems (equations) which are of non-linear and stochastic nature like, stochastic vibrations of beams and columns, noise study in electrical electronics engineering, system dynamics, water resource management, stochastic diffusion equation etc., random sequences and their convergence in numerical algorithms, image processing are becoming important day by day. Thus, fixed point theorems give the conditions under which maps (single or multivalued ) have solutions. The theory itself is a beautiful mixture of analysis (pure and applied), topology, and geometry. Over the last 50 years or so the theory of fixed points has been revealed as a very powerful and important tool in the study of nonlinear phenomena. In particular fixed point techniques have been applied in such diverse fields as biology, chemistry, economics, engineering, game theory, and physics.