Set Valued and Generalized Contraction Mappings in Different Spaces

Functional analysis is an abstract branch of Mathematics that originated from classical analysis. Fixed point theory is one of the important topics of functional analysis. It is a connotation of analysis, topology and geometry. The theory of fixed points has been exposed as a very powerful and important tool in the study of nonlinear phenomena. It has numerous applications in almost all areas of mathematical sciences, for example to prove the existence of solutions of ordinary differential equations, partial differential equations, integral equations, system of linear equations, closed orbit of dynamical systems, variation and linear inequalities, optimization etc. It has very fruitful applications in control theory, game theory, functional equations, mathematical physics, mathematical chemistry, mathematical biology, mathematical economics, approximation theory and many other areas. The concept of fixed point plays a key role in analysis. Thus the study of the fixed point theory has been researched extensively.