|Dr. Ritu Sahni|
The broad area of research has been Functional Analysis which includes topic of research as applications of fixed point theorems, based on fixed points, common fixed points, approximate fixed points, stability of different iterative procedures, theory of iterated function systems (IFS) and iterated multifunction systems (IMS), minimax and saddle point theorems, etc. Most of the real world problems can be easily converted into the mathematical problems for solving linear or nonlinear equations. The importance of the fixed point theory lies mainly in the fact that most of the equations arising in the various physical formulations may be transformed to fixed point equations or inclusions and in that case the existence of a solution is equivalent to the existence of a fixed point for a suitable map. The theorems concerning the properties and existence of fixed points are known as fixed point theorems. These results provide conditions under which maps have solutions. It is an important thrust area of research as it becomes a powerful tool in the study of nonlinear phenomena.
In particular, fixed point techniques play a fundamental role in various theoretical and applied problems such as nonlinear analysis, integral and differential equations, dynamic systems theory, mathematics of fractals and chaos, mathematical economics and mathematical modeling. Its techniques have been applied in such diverse fields as biology, chemistry, mathematical economics (equilibrium problems, game theory, and optimization problems), engineering and physics. Here the aim is to enhance the applications of fixed point theorems to diverse disciplines of mathematics, statistics, engineering and economics, reveal novel aspects of the theory applicable to new situations and explore them for application purpose in other diversified area.
Nonlinear analysis, Dynamic Programming, Numerical methods, Solid Mechanics.